Signal processing apparatus

ABSTRACT

The present invention involves method and apparatus for analyzing measured signals that are modeled as containing primary and secondary portions. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, the present invention involves utilizing a transformation which evaluates a plurality of possible signal coefficients in order to find appropriate coefficients. Alternatively, the present invention involves using statistical functions or Fourier transform and windowing techniques to determine the coefficients relating to two measured signals. Use of this invention is described in particular detail with respect to blood oximetry measurements.

REFERENCE TO PRIOR RELATED APPLICATION

[0001] This application is a divisional of Application No. 10/062,859,filed Jan. 30, 2002, which is a continuation of application Ser. No.09/195,791, filed Nov. 17, 1998, which is a continuation of applicationSer. No. 08/859,837, filed May 16, 1997 (now U.S. Pat. No. 6,157,850),which is a continuation of application Ser. No. 08/320,154, filed Oct.7, 1994 (now U.S. Pat. No. 5,632,272 issued May 27, 1997), which is acontinuation-in-part of application Ser. No. 08/132,812, filed Oct. 6,1993 (now U.S. Pat. No. 5,490,505 issued Feb. 13, 1996), and which is acontinuation-in-part of application Ser. No. 08/249,690 filed May 26,1994 (now U.S. Pat. No. 5,482,036), which is a continuation ofapplication Ser. No. 07/666,060, filed Mar. 7, 1991 (now abandoned).

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to the field of signal processing.More specifically, the present invention relates to the processing ofmeasured signals, containing a primary signal portion and a secondarysignal portion, for the removal or derivation of either the primary orsecondary signal portion when little is known about either of thesecomponents. More particularly, the present invention relates to modelingthe measured signals in a novel way which facilitates minimizing thecorrelation between the primary signal portion and the secondary signalportion in order to produce a primary and/or secondary signal. Thepresent invention is especially useful for physiological monitoringsystems including blood oxygen saturation systems.

[0004] 2. Description of the Related Art

[0005] Signal processors are typically employed to remove or deriveeither the primary or secondary signal portion from a composite measuredsignal including a primary signal portion and a secondary signalportion. For example, a composite signal may contain noise and desirableportions. If the secondary signal portion occupies a different frequencyspectrum than the primary signal portion, then conventional filteringtechniques such as low pass, band pass, and high pass filtering areavailable to remove or derive either the primary or the secondary signalportion from the total signal. Fixed single or multiple notch filterscould also be employed if the primary and/or secondary signal portion(s)exist at a fixed frequency(s).

[0006] It is often the case that an overlap in frequency spectrumbetween the primary and secondary signal portions exists. Complicatingmatters further, the statistical properties of one or both of theprimary and secondary signal portions change with time. In such cases,conventional filtering techniques are ineffective in extracting eitherthe primary or secondary signal. If, however, a description of eitherthe primary or secondary signal portion can be derived, correlationcanceling, such as adaptive noise canceling, can be employed to removeeither the primary or secondary signal portion of the signal isolatingthe other portion. In other words, given sufficient information aboutone of the signal portions, that signal portion can be extracted.

[0007] Conventional correlation cancelers, such as adaptive noisecancelers, dynamically change their transfer function to adapt to andremove portions of a composite signal. However, correlation cancelersrequire either a secondary reference or a primary reference whichcorrelates to either the secondary signal portion only or the primarysignal portion only. For instance, for a measured signal containingnoise and desirable signal, the noise can be removed with a correlationcanceler if a noise reference is available. This is often the case.Although the amplitude of the reference signals are not necessarily thesame as the amplitude of the corresponding primary or secondary signalportions, they have a frequency spectrum which is similar to that of theprimary or secondary signal portions.

[0008] In many cases, nothing or very little is known about thesecondary and/or primary signal portions. One area where measuredsignals comprising a primary signal portion and a secondary signalportion about which no information can easily be determined isphysiological monitoring. Physiological monitoring generally involvesmeasured signals derived from a physiological system, such as the humanbody. Measurements which are typically taken with physiologicalmonitoring systems include electrocardiographs, blood pressure, bloodgas saturation (such as oxygen saturation), capnographs, other bloodconstituent monitoring, heart rate, respiration rate,electro-encephalograph (EEG) and depth of anesthesia, for example. Othertypes of measurements include those which measure the pressure andquantity of a substance within the body such as cardiac output, venousoxygen saturation, arterial oxygen saturation, bilirubin, totalhemoglobin, breathalyzer testing, drug testing, cholesterol testing,glucose testing, extra vasation, and carbon dioxide testing, proteintesting, carbon monoxide testing, and other in-vivo measurements, forexample. Complications arising in these measurements are often due tomotion of the patient, both external and internal (muscle movement,vessel movement, and probe movement, for example), during themeasurement process.

[0009] Many types of physiological measurements can be made by using theknown properties of energy attenuation as a selected form of energypasses through a medium.

[0010] A blood gas monitor is one example of a physiological monitoringsystem which is based upon the measurement of energy attenuated bybiological tissues or substances. Blood gas monitors transmit light intothe test medium and measure the attenuation of the light as a functionof time. The output signal of a blood gas monitor which is sensitive tothe arterial blood flow contains a component which is a waveformrepresentative of the patient's arterial pulse. This type of signal,which contains a component related to the patient's pulse, is called aplethysmographic wave, and is shown in FIG. 1 as curve s.Plethysmographic waveforms are used in blood gas saturationmeasurements. As the heart beats, the amount of blood in the arteriesincreases and decreases, causing increases and decreases in energyattenuation, illustrated by the cyclic wave s in FIG. 1.

[0011] Typically, a digit such as a finger, an ear lobe, or otherportion of the body where blood flows close to the skin, is employed asthe medium through which light energy is transmitted for blood gasattenuation measurements. The finger comprises skin, fat, bone, muscle,etc., shown schematically in FIG. 2, each of which attenuates energyincident on the finger in a generally predictable and constant manner.However, when fleshy portions of the finger are compressed erratically,for example by motion of the finger, energy attenuation becomes erratic.

[0012] An example of a more realistic measured waveform S is shown inFIG. 3, illustrating the effect of motion. The primary plethysmographicwaveform portion of the signal s is the waveform representative of thepulse, corresponding to the sawtooth-like pattern wave in FIG. 1. Thelarge, secondary motion-induced excursions in signal amplitude obscurethe primary plethysmographic signal s. Even small variations inamplitude make it difficult to distinguish the primary signal components in the presence of a secondary signal component n.

[0013] A pulse oximeter is a type of blood gas monitor whichnon-invasively measures the arterial saturation of oxygen in the blood.The pumping of the heat forces freshly oxygenated blood into thearteries causing greater energy attenuation. As well understood in theart, the arterial saturation of oxygenated blood may be determined fromthe depth of the valleys relative to the peaks of two plethysmographicwaveforms measured at separate wavelengths. Patient movement introducesmotion artifacts to the composite signal as illustrated in theplethysmographic waveform illustrated in FIG. 3. These motion artifactsdistort the measured signal.

SUMMARY OF THE INVENTION

[0014] This invention provides improvements upon the methods andapparatus disclosed in U.S. patent application Ser. No. 08/132,812,filed Oct. 6, 1993, entitled Signal Processing Apparatus, which earlierapplication has been assigned to the assignee of the instantapplication. The present invention involves several differentembodiments using the novel signal model in accordance with the presentinvention to isolate either a primary signal portion or a secondarysignal portion of a composite measured signal. In one embodiment, asignal processor acquires a first measured signal and a second measuredsignal that is correlated to the first measured signal. The first signalcomprises a first primary signal portion and a first secondary signalportion. The second signal comprises a second primary signal portion anda second secondary signal portion. The signals may be acquired bypropagating energy through a medium and measuring an attenuated signalafter transmission or reflection. Alternatively, the signals may beacquired by measuring energy generated by the medium.

[0015] In one embodiment, the first and second measured signals areprocessed to generate a secondary reference which does not contain theprimary signal portions from either of the first or second measuredsignals. This secondary reference is correlated to the secondary signalportion of each of the first and second measured signals. The secondaryreference is used to remove the secondary portion of each of the firstand second measured signals via a correlation canceler, such as anadaptive noise canceler. The correlation canceler is a device whichtakes a first and second input and removes from the first input allsignal components which are correlated to the second input. Any unitwhich performs or nearly performs this function is herein considered tobe a correlation canceler.

[0016] An adaptive correlation canceler can be described by analogy to aa reference signal and the measured signals to remove frequencies fromthe measured signals that are also present in the reference signal.Thus, a typical adaptive correlation canceler receives the signal fromwhich it is desired to remove a component and receives a referencesignal of the undesired portion. The output of the correlation canceleris a good approximation to the desired signal with the undesiredcomponent removed.

[0017] Alternatively, the first and second measured signals may beprocessed to generate a primary reference which does not contain thesecondary signal portions from either of the first or second measuredsignals. The primary reference may then be used to remove the primaryportion of each of the first and second measured signals via acorrelation canceler. The output of the correlation canceler is a goodapproximation to the secondary signal with the primary signal removedand may be used for subsequent processing in the same instrument or anauxiliary instrument. In this capacity, the approximation to thesecondary signal may be used as a reference signal for input to a secondcorrelation canceler together with either the first or second measuredsignals for computation of, respectively, either the first or secondprimary signal portions.

[0018] Physiological monitors can benefit from signal processors of thepresent invention. Often in physiological measurements a first signalcomprising a first primary portion and a first secondary portion and asecond signal comprising a second primary portion and a second secondaryportion are acquired. The signals may be acquired by propagating energythrough a patient's body (or a material which is derived from the body,such as breath, blood, or tissue, for example) or inside a vessel andmeasuring an attenuated signal after transmission or reflection.Alternatively, the signal may be acquired by measuring energy generatedby a patient's body, such as in electrocardiography. The signals areprocessed via the signal processor of the present invention to acquireeither a secondary reference or a primary reference which is input to acorrelation canceler, such as an adaptive noise canceler.

[0019] One physiological monitoring apparatus which benefits from thepresent invention is a monitoring system which determines a signal whichis representative of the arterial pulse, called a plethysmographic wave.This signal can be used in blood pressure calculations, bloodconstituent measurements, etc. A specific example of such a use is inpulse oximetry. Pulse oximetry involves determining the saturation ofoxygen in the blood. In this configuration, the primary portion of thesignal is the arterial blood contribution to attenuation of energy as itpasses through a portion of the body where blood flows close to theskin. The pumping of the heart causes blood flow to increase anddecrease in the arteries in a periodic fashion, causing periodicattenuation wherein the periodic waveform is the plethysmographicwaveform representative of the arterial pulse. The secondary portion isnoise. In accordance with the present invention, the measured signalsare modeled such that this secondary portion of the signal is related tothe venous blood contribution to attenuation of energy as it passesthrough the body. The secondary portion also includes artifacts due topatient movement which causes the venous blood to flow in anunpredictable manner, causing unpredictable attenuation and corruptingthe otherwise periodic plethysmographic waveform. Respiration alsocauses the secondary or noise portion to vary, although typically at alower frequency than the patients pulse rate. Accordingly, the measuredsignal which forms a plethysmographic waveform is modeled in accordancewith the present invention such that the primary portion of the signalis representative of arterial blood contribution to attenuation and thesecondary portion is due to several other parameters.

[0020] A physiological monitor particularly adapted to pulse oximetryoxygen saturation measurement comprises two light emitting diodes(LED's) which emit light at different wavelengths to produce first andsecond signals. A detector registers the attenuation of the twodifferent energy signals after each passes through an absorptive media,for example a digit such as a finger, or an earlobe. The attenuatedsignals generally comprise both primary (arterial attenuator) andsecondary (noise) signal portions. A static filtering system, such as abandpass filter, removes a portion of the secondary signal which isoutside of a known bandwidth of interest, leaving an erratic or randomsecondary signal portion, often caused by motion and often difficult toremove, along with the primary signal portion.

[0021] A processor in accordance with one embodiment of the presentinvention removes the primary signal portions from the measured signalsyielding a secondary reference which is a combination of the remainingsecondary signal portions. The secondary reference is correlated to bothof the secondary signal portions. The secondary reference and at leastone of the measured signals are input to a correlation canceler, such asan adaptive noise canceler, which removes the random or erratic portionof the secondary signal. This yields a good approximation to a primaryplethysmographic signal as measured at one of the measured signalwavelengths. As is known in the art, quantitative measurements of theamount of oxygenated arterial blood in the body can be determined fromthe plethysmographic signal in a variety of ways.

[0022] The processor of the present invention may also remove thesecondary signal portions from the measured signals yielding a primaryreference which is a combination of the remaining primary signalportions. The primary reference is correlated to both of the primarysignal portions. The primary reference and at least one of the measuredsignals are input to a correlation canceler which removes the primaryportions of the measured signals. This yields a good approximation tothe secondary signal at one of the measured signal wavelengths. Thissignal may be useful for removing secondary signals from an auxiliaryinstrument as well as determining venous blood oxygen saturation.

[0023] In accordance with the signal model of the present invention, thetwo measured signals each having primary and secondary signal portionscan be related by coefficients. By relating the two equations withrespect to coefficients defined in accordance with the presentinvention, the coefficients provide information about the arterialoxygen saturation and about the noise (the venous oxygen saturation andother parameters). In accordance with this aspect of the presentinvention, the coefficients can be determined by minimizing thecorrelation between the primary and secondary signal portions as definedin the model. Accordingly, the signal model of the present invention canbe utilized in many ways in order to obtain information about themeasured signals as will be further apparent in the detailed descriptionof the preferred embodiments.

[0024] One aspect of the present invention is a method for use in asignal processor in a signal processor for processing at least twomeasured signals S₁ and S₂ each containing a primary signal portion sand a secondary signal portion n, the signals S₁ and S₂ being inaccordance with the following relationship:

S ₁ =s ₁ +n ₁

S ₂=s₂ +n ₂

[0025] where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂

[0026] and where r_(a) and r_(v) are coefficients.

[0027] The method comprises a number of steps. A value of coefficientr_(a) is determined which minimize correlation between s₁ and n₁. Then,at least one of the first and second signals is processed using thedetermined value for r_(a) to significantly reduce n from at least oneof the first or second measured signal to form a clean signal.

[0028] In one embodiment, the clean signal is displayed on a display. Inanother embodiment, wherein the first and second signals arephysiological signals, the method further comprises the step ofprocessing the clean signal to determine a physiological parameter fromthe first or second measured signals. In one embodiment, the parameteris arterial oxygen saturation. In another embodiment, the parameter isan ECG signal. In yet another embodiment, wherein the first portion ofthe measured signals is indicative of a heart plethysmograph, the methodfurther comprises the step of calculating the pulse rate.

[0029] Another aspect of the present invention involves a physiologicalmonitor. The monitor has a first input configured to receive a firstmeasured signal S₁ having a primary portion, s₁, and a secondary portionn₁. The monitor also has a second input configured to received a secondmeasured signal S₂ having a primary portion s₂ and a secondary portionn₂. Advantageously, the first and the second measured signals S₁ and S₂are in accordance with the following relationship:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

[0030] where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂

[0031] and where r_(a) and r_(v) are coefficients.

[0032] The monitor further has a scan reference processor, the scanreference processor responds to a plurality of possible values for r_(a)to multiply the second measured signal by each of the possible valuesfor ra and for each of the resulting values, to subtract the resultingvalues from the first measured signal to provide a plurality of outputsignals. A correlation canceler having a first input configured toreceive the first measured signal, and having a second input configuredto receive the plurality of output signals from the saturation scanreference processor, provides a plurality of output vectorscorresponding to the correlation cancellation between the plurality ofoutput signals and the first measured signal. An integrator having aninput configured to receive the plurality of output vectors from thecorrelation canceler is responsive to the plurality of output vectors todetermine a corresponding power for each output vector. An extremumdetector is coupled at its input to the output of the integrator. Theextremum detector is responsive to the corresponding power for eachoutput vector to detect a selected power.

[0033] In one embodiment, the plurality of possible values correspond toa plurality of possible values for a selected blood constituent. In oneembodiment the, the selected blood constituent is arterial blood oxygensaturation. In another embodiment, the selected blood constituent isvenous blood oxygen saturation. In yet another embodiment, the selectedblood constituent is carbon monoxide.

[0034] Another aspect of the present invention involves a physiologicalmonitor. The monitor has a first input configured to receive a firstmeasured signal S₁ having a primary portion, s₁, and a secondaryportion, n₁. The monitor also has a second input configured to receiveda second measured signal S₂ having a primary portion s₂ and a secondaryportion n₂. The first and the second measured signals S₁ and S₂ are inaccordance with the following relationship:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

[0035] where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a)s₂ and n ₁ =r _(v) n _(s)

[0036] and where r_(a) and r_(v) are coefficients.

[0037] A transform module is responsive to the first and the secondmeasured signals and responsive to a plurality of possible values forr_(a) to provide at least one power curve as an output. An extremumcalculation module is responsive to the at least one power curve toselect a value for r_(a) which minimizes the correlation between s andn, and to calculate from the value for r_(a) a corresponding saturationvalue as an output. A display module is responsive to the output ofsaturation calculation to display the saturation value.

BRIEF DESCRIPTION OF THE DRAWINGS

[0038]FIG. 1 illustrates an ideal plethysmographic waveform.

[0039]FIG. 2 schematically illustrates a typical finger.

[0040]FIG. 3 illustrates a plethysmographic waveform which includes amotion-induced erratic signal portion.

[0041]FIG. 4a illustrates a schematic diagram of a physiological monitorto compute primary physiological signals.

[0042]FIG. 4b illustrates a schematic diagram of a physiological monitorto compute secondary signals.

[0043]FIG. 5a illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute primaryphysiological signals.

[0044]FIG. 5b illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute secondarymotion artifact signals.

[0045]FIG. 5c illustrates the transfer function of a multiple notchfilter.

[0046]FIG. 6a illustrates a schematic of absorbing material comprising Nconstituents within the absorbing material.

[0047]FIG. 6b illustrates another schematic of absorbing materialcomprising N constituents, including one mixed layer, within theabsorbing material.

[0048]FIG. 6c illustrates another schematic of absorbing materialcomprising N constituents, including two mixed layers, within theabsorbing material.

[0049]FIG. 7a illustrates a schematic diagram of a monitor, to computeprimary and secondary signals in accordance with one aspect of thepresent invention.

[0050]FIG. 7b illustrates the ideal correlation canceler energy or poweroutput as a function of the signal coefficients r₁, r₂, . . . r_(n). Inthis particular example, r₃=r_(a) and r₇=r_(v).

[0051]FIG. 7c illustrates the non-ideal correlation canceler energy orpower output as a function of the signal coefficients r₁, r₂, . . .r_(n). In this particular example, r₃=r_(a) and r₇=r_(v).

[0052]FIG. 8 is a schematic model of a joint process estimatorcomprising a least-squares lattice predictor and a regression filter.

[0053]FIG. 8a is a schematic model of a joint process estimatorcomprising a QRD least-squares lattice (LSL) predictor and a regressionfilter.

[0054]FIG. 9 is a flowchart representing a subroutine for implementingin software a joint process estimator as modeled in FIG. 8.

[0055]FIG. 9a is a flowchart representing a subroutine for implementingin software a joint process estimator as modeled in FIG. 8a.

[0056]FIG. 10 is a schematic model of a joint process estimator with aleast-squares lattice predictor and two regression filters.

[0057]FIG. 10a is a schematic model of a joint process estimator with aQRD least-squares lattice predictor and two regression filters.

[0058]FIG. 11 is an example of a physiological monitor in accordancewith the teachings of one aspect of the present invention.

[0059]FIG. 11a illustrates an example of a low noise emitter currentdriver with accompanying digital to analog converter.

[0060]FIG. 12 illustrates the front end analog signal conditioningcircuitry and the analog to digital conversion circuitry of thephysiological monitor of FIG. 11.

[0061]FIG. 13 illustrates further detail of the digital signalprocessing circuitry of FIG. 11.

[0062]FIG. 14 illustrates additional detail of the operations performedby the digital signal processing circuitry of FIG. 11.

[0063]FIG. 15 illustrates additional detail regarding the demodulationmodule of FIG. 14.

[0064]FIG. 16 illustrates additional detail regarding the decimationmodule of FIG. 14.

[0065]FIG. 17 represents a more detailed block diagram of the operationsof the statistics module of FIG. 14.

[0066]FIG. 18 illustrates a block diagram of the operations of oneembodiment of the saturation transform module of FIG. 14.

[0067]FIG. 19 illustrates a block diagram of the operation of thesaturation calculation module of FIG. 14.

[0068]FIG. 20 illustrates a block diagram of the operations of the pulserate calculation module of FIG. 14.

[0069]FIG. 21 illustrates a block diagram of the operations of themotion artifact suppression module of FIG. 20.

[0070]FIG. 21a illustrates an alternative block diagram for theoperations of the motion artifact suppression module of FIG. 20.

[0071]FIG. 22 illustrates a saturation transform curve in accordancewith the principles of the present invention.

[0072]FIG. 23 illustrates a block diagram of an alternative embodimentto the saturation transform in order to obtain a saturation value.

[0073]FIG. 24 illustrates a histogram saturation transform in accordancewith the alternative embodiment of FIG. 23.

[0074]FIGS. 25A-25C illustrate yet another alternative embodiment inorder to obtain the saturation.

[0075]FIG. 26 illustrates a signal measured at a red wavelengthλa=λred=660 nm for use in a processor of the present invention fordetermining the secondary reference n′(t) or the primary reference s′(t)and for use in a correlation canceler. The measured signal comprises aprimary portion s_(λa)(t) and a secondary portion n_(λa)(t).

[0076]FIG. 27 illustrates a signal measured at an infrared wavelengthλb=λ_(IR)=910 nm for use in a processor of the present invention fordetermining the secondary reference n′(t) or the primary reference s′(t)and for use in a correlation canceler. The measured signal comprises aprimary portion s_(λb)(t) and a secondary portion n_(λb)(t).

[0077]FIG. 28 illustrates the secondary reference n′(t) determined by aprocessor of the present invention.

[0078]FIG. 29 illustrates a good approximation s″_(λa)(t) to the primaryportion s_(λa)(t) of the signal S_(λa)(t) measured at λa=λred=660 nmestimated by correlation cancellation with a secondary reference n′(t).

[0079]FIG. 30 illustrates a good approximation s″_(λb)(t) to the primaryportion s_(λb)(t) of the signal S_(λb)(t) measured at λb=λIR=910 nmestimated by correlation cancellation with a secondary reference n′(t).

[0080]FIG. 31 depicts a set of 3 concentric electrodes, i.e., a tripolarelectrode sensor, to derive electrocardiography (ECG) signals, denotedas S₁, S₂ and S₃, for use with the present invention. Each of the ECGsignals contains a primary portion and a secondary portion.

DETAILED DESCRIPTION OF THE INVENTION

[0081] The present invention involves a system which utilizes first andsecond measured signals that each contain a primary signal portion and asecondary signal portion. In other words, given a first and secondcomposite signals S₁(t)=s₁(t)+n₁(t) and S₂(t)=s₂(t)+n₂(t), the system ofthe present invention can be used to isolate either the primary signalportion s(t) or the secondary signal portion n(t). Following processing,the output of the system provides a good approximation n″(t) to thesecondary signal portion n(t) or a good approximation s″(t) to theprimary signal portion s(t).

[0082] The system of the present invention is particularly useful wherethe primary and/or secondary signal portion n(t) may contain one or moreof a constant portion, a predictable portion, an erratic portion, arandom portion, etc. The primary signal approximation s″(t) or secondarysignal approximation n″(t) is derived by removing as many of thesecondary signal portions n(t) or primary signal portions s(t) from thecomposite signal S(t) as possible. The remaining signal forms either theprimary signal approximation s″(t) or secondary signal approximationn″(t), respectively. The constant portion and predictable portion of thesecondary signal n(t) are easily removed with traditional filteringtechniques, such as simple subtraction, low pass, band pass, and highpass filtering. The erratic portion is more difficult to remove due toits unpredictable nature. If something is known about the erraticsignal, even statistically, it could be removed, at least partially,from the measured signal via traditional filtering techniques. However,often no information is known about the erratic portion of the secondarysignal n(t). In this case, traditional filtering techniques are usuallyinsufficient.

[0083] In order to remove the secondary signal n(t), a signal model inaccordance with the present invention is defined as follows for thefirst and second measured signals S₁ and S₂:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

[0084] with s₁=r_(a)s₂ and n₁=r_(v)n₂ or$r_{a} = {{\frac{s_{1}}{s_{2}}\quad {and}\quad n_{1}} = \frac{n_{1}}{n_{2}}}$

[0085] where s₁ and n₁ are at least somewhat (preferably substantially)uncorrelated and s₂ and n₂ are at least somewhat (preferablysubstantially) uncorrelated. The first and second measured signals S₁and S₂ are related by correlation coefficients r_(a) and r_(v) asdefined above. The use and selection of these coefficients is describedin further detail below.

[0086] In accordance with one aspect of the present invention, thissignal model is used in combination with a correlation canceler, such asan adaptive noise canceler, to remove or derive the erratic portion ofthe measured signals.

[0087] Generally, a correlation canceler has two signal inputs and oneoutput. One of the inputs is either the secondary reference n′(t) or theprimary reference s′(t) which are correlated, respectively, to thesecondary signal portions n(t) and the primary signal portions s(t)present in the composite signal S(t). The other input is for thecomposite signal S(t). Ideally, the output of the correlation cancelers″(t) or n″(t) corresponds, respectively, to the primary signal s(t) orthe secondary signal n(t) portions only. Often, the most difficult taskin the application of correlation cancelers is determining the referencesignals n′(t) and s′(t) which are correlated to the secondary n(t) andprimary s(t) portions, respectively, of the measured signal S(t) since,as discussed above, these portions are quite difficult to isolate fromthe measured signal S(t). In the signal processor of the presentinvention, either a secondary reference n′(t) or a primary references′(t) is determined from two composite signals measured simultaneously,or nearly simultaneously, at two different wavelengths, λa and ζb.

[0088] A block diagram of a generic monitor incorporating a signalprocessor according to the present invention, and a correlation canceleris shown in FIGS. 4a and 4 b. Two measured signals, S_(λa)(t) andS_(λb)(t), are acquired by a detector 20. One skilled in the art willrealize that for some physiological measurements, more than one detectormay be advantageous. Each signal is conditioned by a signal conditioner22 a and 22 b. Conditioning includes, but is not limited to, suchprocedures as filtering the signals to remove constant portions andamplifying the signals for ease of manipulation. The signals are thenconverted to digital data by an analog-to-digital converter 24 a and 24b. The first measured signal S_(λa)(t) comprises a first primary signalportion, labeled herein S_(λa)(t), and a first secondary signal portion,labeled herein n_(λa)(t). The second measured signal S_(λb)(t) is atleast partially correlated to the first measured signal S_(λa)(t) andcomprises a second primary signal portion, labeled herein s_(λb)(t), anda second secondary signal portion, labeled herein n_(λb)(t). Typicallythe first and second secondary signal portions, n_(λa)(t) and n_(λb)(t),are uncorrelated and/or erratic with respect to the primary signalportions s_(λa)(t) and s_(λb)(t). The secondary signal portionsn_(λa)(t) and n_(λb)(t) are often caused by motion of a patient inphysiological measurements.

[0089] The signals S_(λa)(t) and S_(λb)(t) are input to a referenceprocessor 26. The reference processor 26 multiplies the second measuredsignal S_(λb)(t) by either a factor r_(a)=s_(λa)(t)/s_(λb)(t) or afactor r_(v)=n_(λa)(t)/n_(λb)(t) and then subtracts the second measuredsignal S_(λb)(t) from the first measured signal S_(λa)(t). The signalcoefficient factors r_(a) and r_(v) are determined to cause either theprimary signal portions s_(λa)(t) and s_(λb)(t) or the secondary signalportions n_(λa)(t) and n_(λb)(t) to cancel, respectively, when the twosignals S_(λa)(t) and S_(λb)(t) are subtracted. Thus, the output of thereference processor 26 is either a secondary reference signaln′(t)=n_(λa)(t)−r_(a)n_(λb)(t), in FIG. 4a, which is correlated to bothof the secondary signal portions n_(λa)(t) and n_(λb)(t) or a primaryreference signal s′(t)=s_(λa)(t)−r_(v)s_(λb)(t), in FIG. 4b, which iscorrelated to both of the primary signal portions S_(λa)(t) ands_(λb)(t). A reference signal n′(t) or s′(t) is input, along with one ofthe measured signals S_(λa)(t) or S_(λb)(t), to a correlation canceler27 which uses the reference signal n′(t) or s′(t) to remove either thesecondary signal portions n_(λa)(t) or n_(λb)(t) or the primary signalportions s_(λa)(t) or s_(λb)(t) from the measured signal S_(λa)(t) orS_(λb)(t). The output of the correlation canceler 27 is a good primarysignal approximation s″(t) or secondary signal approximation n″(t). Inone embodiment, the approximation s″(t) or n″(t) is displayed on adisplay 28.

[0090] In one embodiment, an adaptive noise canceler 30, an example ofwhich is shown in block diagram form in FIG. 5a, is employed as thecorrelation canceler 27, to remove either one of the erratic, secondarysignal portions n_(λa)(t) and n_(λb)(t) from the first and secondsignals S_(λa)(t) and S_(λb)(t). The adaptive noise canceler 30 in FIG.5a has as one input a sample of the secondary reference n′(t) which iscorrelated to the secondary signal portions n_(λa)(t) and n_(λb)(t). Thesecondary reference n′(t) is determined from the two measured signalsS_(λa)(t) and S_(λb)(t) by the processor 26 of the present invention asdescribed herein. A second input to the adaptive noise canceler, is asample of either the first or second composite measured signalsS_(λa)(t)=s_(λa)(t)+n_(λa)(t) or S_(λb)(t)=s_(λb)(t)+n_(λb)(t).

[0091] The adaptive noise canceler 30, in FIG. 5b, may also be employedto remove either one of primary signal portions s_(λa)(t) and s_(λb)(t)from the first and second measured signals S_(λa)(t) and S_(λb)(t). Theadaptive noise canceler 30 has as one input a sample of the primaryreference s′(t) which is correlated to the primary signal portionss_(λa)(t) and s_(λb)(t). The primary reference s′(t) is determined fromthe two measured signals S_(λa)(t) and S_(λb)(t) by the processor 26 ofthe present invention as described herein. A second input to theadaptive noise canceler 30 is a sample of either the first or secondmeasured signals S_(λa)(t)=s_(λa)(t)+n_(λa)(t) orS_(λb)(t)=s_(λb)(t)+n_(λb)(t).

[0092] The adaptive noise canceler 30 functions to remove frequenciescommon to both the reference n′(t) or s′(t) and the measured signalS_(λa)(t) or S_(λb)(t). Since the reference signals are correlated toeither the secondary signal portions n_(λa)(t) and n_(λb)(t) or theprimary signal portions s_(λa)(t) and s_(λb)(t), the reference signalswill be correspondingly erratic or well behaved. The adaptive noisecanceler 30 acts in a manner which may be analogized to a dynamicmultiple notch filter based on the spectral distribution of thereference signal n′(t) or s′(t).

[0093]FIG. 5c illustrates an exemplary transfer function of a multiplenotch filter. The notches, or dips in the amplitude of the transferfunction, indicate frequencies which are attenuated or removed when asignal passes through the notch filter. The output of the notch filteris the composite signal having frequencies at which a notch is presentremoved. In the analogy to an adaptive noise canceler 30, thefrequencies at which notches are present change continuously based uponthe inputs to the adaptive noise canceler 30.

[0094] The adaptive noise canceler 30 (FIGS. 5a and 5 b) produces anoutput signal, labeled herein as s″_(λa)(t), s″_(λb)(t), n″_(λa)(t) orn″_(λb)(t) which is fed back to an internal processor 32 within theadaptive noise canceler 30. The internal processor 32 automaticallyadjusts its own transfer function according to a predetermined algorithmsuch that the output of the internal processor 32 labeled b_(λ)(t) inFIGS. 5a and c _(λ)(t) in FIG. 5b, closely resembles either thesecondary signal portion nλ_(a)(t) or n_(λb)(t) or the primary signalportion s_(λa)(t) or s_(λb)(t). The output b(t) of the internalprocessor 32 in FIG. 5a is subtracted from the measured signal,S_(λa)(t) or S_(λb)(t), yielding a signal outputs″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−b_(λa)(t) or a signal outputs″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−b_(λb)(t). The internal processoroptimizes s″_(λa)(t) or s″_(λb)(t) such that s″_(λa)(t) or s″_(λb)(t) isapproximately equal to the primary signal s_(λa)(t) or s_(λb)(t),respectively. The output c_(λ)(t) of the internal processor 32 in FIG.5b is subtracted from the measured signal, S_(λa)(t) or S_(λb)(t),yielding a signal output given byn″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−c_(λa)(t) or a signal output given byn″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−c_(λb)(t). The internal processoroptimizes n″_(λa)(t) or n″_(λb)(t) such that n″_(λa)(t) or n″_(λb)(t) isapproximately equal to the secondary signal portion n_(λa)(t) orn_(λb)(t), respectively.

[0095] One algorithm which may be used for the adjustment of thetransfer function of the internal processor 32 is a least-squaresalgorithm, as described in Chapter 6 and Chapter 12 of the book AdaptiveSignal Processing by Bernard Widrow and Samuel Stearns, published byPrentice Hall, copyright 1985. This entire book, including Chapters 6and 12, is hereby incorporated herein by reference.

[0096] Adaptive processors 30 in FIGS. 5a and 5 b have been successfullyapplied to a number of problems including antenna sidelobe canceling,pattern recognition, the elimination of periodic interference ingeneral, and the elimination of echoes on long distance telephonetransmission lines. However, considerable ingenuity is often required tofind a suitable reference signal n′(t) or s′(t) since the portionsn_(λa)(t), n_(λb)(t), s_(λa)(t) and s_(λb)(t) cannot easily be separatedfrom the measured composite signals s_(λa)(t) and s_(λb)(t). If eitherthe actual secondary portion n_(λa)(t) or n_(λb)(t) or the primarysignal portion s_(λa)(t) or s_(λb)(t) were a priori available,techniques such as correlation cancellation would not be necessary.

Generalized Determination of Primary and Secondary Reference Signals

[0097] An explanation which describes how the reference signals n′(t)and s′(t) may be determined follows. A first signal is measured at, forexample, a wavelength λa, by a detector yielding a signal S_(λa)(t):

S _(λa)(t)=s _(λa)(t)+n _(λa)(t)  (1)

[0098] where s_(λa)(t) is the primary signal portion and n_(λa)(t) isthe secondary signal portion.

[0099] A similar measurement is taken simultaneously, or nearlysimultaneously, at a different wavelength, b, yielding:

S _(λb)(t)=s _(λb)(t)+n_(λb)(t)  (2)

[0100] Note that as long as the measurements, S_(λa)(t) and S_(λb)(t),are taken substantially simultaneously, the secondary signal components,n_(λa)(t) and n_(λb)(t), are correlated because any random or erraticfunctions affect each measurement in nearly the same fashion. Thesubstantially predictable primary signal components, s_(λa)(t) ands_(λb)(t), are also correlated to one another.

[0101] To obtain the reference signals n′(t) and s′(t), the measuredsignals S_(λa)(t) and S_(λb)(t) are transformed to eliminate,respectively, the primary or secondary signal components. In accordancewith the present invention one way of doing this is to findproportionality constants, r_(a and r) _(v), between the primary signalportions s_(λa)(t) and s_(λb)(t) and the secondary signal portionsn_(λa)(t) and n_(λb)(t) such that the signals can be modeled as follows:

s _(λa)(t)=r _(a) s _(λb)(t)

n _(λa)(t)=r _(v) n _(λb)(t)  (3)

[0102] In accordance with the inventive signal model of the presentinvention, these proportionality relationships can be satisfied in manymeasurements, including but not limited to absorption measurements andphysiological measurements. Additionally, in accordance with the signalmodel of the present invention, in most measurements, theproportionality constants r_(a and r) _(v) can be determined such that:

n _(λa)(t)≠r_(a) n _(λb)(t)

s _(λa)(t)≠r _(v) s _(λb)(t).

[0103] Multiplying equation (2) by r_(a) and then subtracting equation(2) from equation (1) results in a single equation wherein the primarysignal terms s_(λa)(t) and s_(λb)(t) cancel:

n′(t)=S _(λa)(t)−r _(a) S _(λb)(t)=n _(λa)(t)−r _(a) n _(λb)(t);  (5a)

[0104] a non-zero signal which is correlated to each secondary signalportion n_(λa)(t) and n_(λb)(t) and can be used as the secondaryreference n′(t) in a correlation canceler such as an adaptive noisecanceler.

[0105] Multiplying equation (2) by r_(v) and then subtracting equation(2) from equation (1) results in a single equation wherein the secondarysignal terms n_(λa)(t) and n_(λb)(t) cancel, leaving:

s′(t)=S _(λa)(t)−r _(v) S _(λb)(t)=s _(λa)(t)−r _(v) s _(λb)(t);  (5b)

[0106] a non-zero signal which is correlated to each of the primarysignal portions s_(λa)(t) and s_(λb)(t) and can be used as the signalreference s′(t) in a correlation canceler such as an adaptive noisecanceler.

EXAMPLE OF DETERMINATION OF PRIMARY AND SECONDARY REFERENCE SIGNALS INAN ABSORPTIVE SYSTEM

[0107] Correlation canceling is particularly useful in a large number ofmeasurements generally described as absorption measurements. An exampleof an absorption type monitor which can advantageously employcorrelation canceling, such as adaptive noise canceling, based upon areference n′(t) or s′(t) determined by a processor of the presentinvention is one which determines the concentration of an energyabsorbing constituent within an absorbing material when the material issubject to change. Such changes can be caused by forces about whichinformation is desired or primary, or alternatively, by random orerratic secondary forces such as a mechanical force on the material.Random or erratic interference, such as motion, generates secondarycomponents in the measured signal. These secondary components can beremoved or derived by the correlation canceler if a suitable secondaryreference n′(t) or primary reference s′(t) is known.

[0108] A schematic N constituent absorbing material comprising acontainer 42 having N different absorbing constituents, labeled A₁, A₂,A₃, . . . A_(N), is shown in FIG. 6a. The constituents A₁ through A_(N)in FIG. 6a are arranged in a generally orderly, layered fashion withinthe container 42. An example of a particular type of absorptive systemis one in which light energy passes through the container 42 and isabsorbed according to the generalized Beer-Lambert Law of lightabsorption. For light of wavelength λa, this attenuation may beapproximated by: $\begin{matrix}{I = {I_{o}{\exp \left( {- {\sum\limits_{i = 1}^{N}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}x_{i}}}} \right)}}} & (6)\end{matrix}$

[0109] Initially transforming the signal by taking the natural logarithmof both sides and manipulating terms, the signal is transformed suchthat the signal components are combined by addition rather thanmultiplication, i.e.: $\begin{matrix}{S_{\lambda \quad a} = {{\ln \left( {I_{o}/I} \right)} = {\sum\limits_{i = 1}^{N}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}x_{i}}}}} & (7)\end{matrix}$

[0110] where I₀ is the incident light energy intensity; I is thetransmitted light energy intensity; ε_(i,λa) is the absorptioncoefficient of the i^(th) constituent at the wavelength λa; x_(i)(t) isthe optical path length of i^(th) layer, i.e., the thickness of materialof the i^(th) layer through which optical energy passes; and c_(i)(t) isthe concentration of the i^(th) constituent in the volume associatedwith the thickness x_(i)(t). The absorption coefficients ε₁ throughε_(N) are known values which are constant at each wavelength. Mostconcentrations c₁(t) through c_(N)(t) are typically unknown, as are mostof the optical path lengths x_(i)(t) of each layer. The total opticalpath length is the sum of each of the individual optical path lengthsx_(i)(t) of each layer.

[0111] When the material is not subject to any forces which cause changein the thicknesses of the layers, the optical path length of each layer,x_(i)(t), is generally constant. This results in generally constantattenuation of the optical energy and thus, a generally constant offsetin the measured signal. Typically, this offset portion of the signal isof little interest since knowledge about a force which perturbs thematerial is usually desired. Any signal portion outside of a knownbandwidth of interest, including the constant undesired signal portionresulting from the generally constant absorption of the constituentswhen not subject to change, is removed. This is easily accomplished bytraditional band pass filtering techniques. However, when the materialis subject to forces, each layer of constituents may be affected by theperturbation differently than other layers. Some perturbations of theoptical path lengths of each layer x_(i)(t) may result in excursions inthe measured signal which represent desired or primary information.Other perturbations of the optical path length of each layer x_(i)(t)cause undesired or secondary excursions which mask primary informationin the measured signal. Secondary signal components associated withsecondary excursions must also be removed to obtain primary informationfrom the measured signal. Similarly, the ability to compute secondarysignal components caused by secondary excursions directly allows one toobtain primary signal components from the measured signal via simplesubtraction, or correlation cancellation techniques.

[0112] The correlation canceler may selectively remove from thecomposite signal, measured after being transmitted through or reflectedfrom the absorbing material, either the secondary or the primary signalcomponents caused by forces which perturb or change the materialdifferently from the forces which perturbed or changed the material tocause respectively, either the primary or secondary signal component.For the purposes of illustration, it will be assumed that the portion ofthe measured signal which is deemed to be the primary signal s_(λa)(t)is the attenuation term ε₅c₅x₅(t) associated with a constituent ofinterest, namely A₅, and that the layer of constituent A₅ is affected byperturbations different than each of the layers of other constituents A₁through A₄ and A₆ through A_(N). An example of such a situation is whenlayer A₅ is subject to forces about which information is deemed to beprimary and, additionally, the entire material is subject to forceswhich affect each of the layers. In this case, since the total forceaffecting the layer of constituent A₅ is different than the total forcesaffecting each of the other layers and information is deemed to beprimary about the forces and resultant perturbation of the layer ofconstituent A₅, attenuation terms due to constituents A₁ through A₄ andA₆ through A_(N) make up the secondary signal portion n_(λa)(t). Even ifthe additional forces which affect the entire material cause the sameperturbation in each layer, including the layer of A₅, the total forceson the layer of constituent A₅ cause it to have different totalperturbation than each of the other layers of constituents A₁ through A₄and A₆ through A_(N).

[0113] It is often the case that the total perturbation affecting thelayers associated with the secondary signal components is caused byrandom or erratic forces. This causes the thickness of layers to changeerratically and the optical path length of each layer, x_(i)(t), tochange erratically, thereby producing a random or erratic secondarysignal component n_(λa)(t). However, regardless of whether or not thesecondary signal portion n_(λa)(t) is erratic, the secondary signalcomponent n_(λa)(t) can be either removed or derived via a correlationcanceler, such as an adaptive noise canceler, having as one input,respectively, a secondary reference n′(t) or a primary reference s′(t)determined by a processor of the present invention as long as theperturbation on layers other than the layer of constituent A₅ isdifferent than the perturbation on the layer of constituent A₅. Thecorrelation canceler yields a good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t). In the event that anapproximation to the primary signal is obtained, the concentration ofthe constituent of interest, c₅(t), can often be determined since insome physiological measurements, the thickness of the primary signalcomponent, x₅(t) in this example, is known or can be determined.

[0114] The correlation canceler utilizes either the secondary referencen′(t) or the primary reference s′(t) determined from two substantiallysimultaneously measured signals S_(λa)(t) and S_(λb)(t). S_(λa)(t) isdetermined as above in equation (7). S_(λb)(t) is determined similarlyat a different wavelength b. To find either the secondary referencen′(t) or the primary reference s′(t), attenuated transmitted energy ismeasured at the two different wavelengths a and b and transformed vialogarithmic conversion. The signals S_(λa)(t) and S_(λb)(t) can then bewritten (logarithm converted) as: $\begin{matrix}{{S_{\lambda \quad a}(t)} = {{\varepsilon_{5,{\lambda \quad a}}c_{5}{x_{5}(t)}} + {\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}x_{i}}} + {\sum\limits_{i = 6}^{N}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}x_{i}}}}} & (8)\end{matrix}$

 S _(λa)(t)=ε_(5,λa) c ₅ x ₅(t)+n _(λa)(t)  (9) $\begin{matrix}{S_{\lambda \quad {b{(t)}}} = {{\varepsilon_{5,{\lambda \quad b}}c_{5}{x_{5}(t)}} + {\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i,{\lambda \quad b}}c_{i}x_{i}}} + {\sum\limits_{i = 6}^{N}\quad {\varepsilon_{i,{\lambda \quad b}}c_{i}x_{i}}}}} & (10)\end{matrix}$

 S _(λb)(t)=ε_(5,λb) c ₅ x ₅(t)+n _(λb)(t)  (11)

[0115] Further transformations of the signals are the proportionalityrelationships in accordance with the signal model of the presentinvention defining ra and rv, similar to equation (3), which allowsdetermination of a noise reference n′(t) and a primary reference s′(t).These are:

ε_(5,λa) =r _(a)ε_(5,λb)  (12a)

n _(λa) =r _(v) n _(λb)  (12b)

[0116] where

n _(λa) ≠r _(a) n _(λb)  (13a)

ε_(5,λa) ≠r _(v)ε_(5,λb)  (13b)

[0117] It is often the case that both equations (12) and (13) can besimultaneously satisfied. Multiplying equation (11) by r_(a) andsubtracting the result from equation (9) yields a non-zero secondaryreference which is a linear sum of secondary signal components:$\begin{matrix}\begin{matrix}{{n^{\prime}(t)} = {{S_{\lambda \quad a}(t)} - {r_{a}{S_{\lambda \quad b}(t)}}}} \\{= {{n_{\lambda \quad a}(t)} - {r_{a}{n_{\lambda \quad b}(t)}}}}\end{matrix} & \left( {14\text{a}} \right) \\\begin{matrix}{\quad {= {{\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}{x_{i}(t)}}} + {\sum\limits_{i + 6}^{N}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}{x_{i}(t)}}} -}}} \\{{{\sum\limits_{i = 1}^{4}\quad {r_{a}\varepsilon_{i,{\lambda \quad b}}c_{i}{x_{i}(t)}}} + {\sum\limits_{i = 6}^{N}\quad {r_{a}\varepsilon_{i,{\lambda \quad b}}c_{i}{x_{i}(t)}}}}}\end{matrix} & \left( {15\text{a}} \right) \\\begin{matrix}{\quad {= {{\sum\limits_{i = 1}^{4}{c_{i}{{x_{i}(t)}\left\lbrack {\varepsilon_{i,{\lambda \quad a}} - {r_{a}\varepsilon_{i,{\lambda \quad a}}} - {r_{a}\varepsilon_{i,{\lambda \quad b}}}} \right\rbrack}}} +}}} \\{{\sum\limits_{i = 6}^{N}{c_{i}{{x_{i}(t)}\left\lbrack {\varepsilon_{1,{\lambda \quad a}} - {r_{a}\varepsilon_{i,{\lambda \quad b}}}} \right\rbrack}}}}\end{matrix} & \left( {16\text{a}} \right)\end{matrix}$

[0118] Multiplying equation (11) by r_(v) and subtracting the resultfrom equation (9) yields a primary reference which is a linear sum ofprimary signal components: $\begin{matrix}{{s^{\prime}(t)} = {{{S_{\lambda \quad a}(t)} - {r_{v}{S_{\lambda \quad b}(t)}}} = {{s_{\lambda \quad a}(t)} - {r_{v}{s_{\lambda \quad b}(t)}}}}} & \left( {14b} \right) \\{\quad {= {{c_{5}{x_{5}(t)}ɛ_{5,{\lambda \quad a}}} - {r_{v}c_{5}{x_{5}(t)}ɛ_{5,{\lambda \quad b}}}}}} & \left( {15b} \right) \\{\quad {= {c_{5}{{{x_{5}(t)}\left\lbrack {ɛ_{5,{\lambda \quad a}} - {r_{v}ɛ_{5,{\lambda \quad b}}}} \right\rbrack}.}}}} & \left( {16b} \right)\end{matrix}$

[0119] A sample of either the secondary reference n′(t) or the primaryreference s′(t), and a sample of either measured signal S_(λa)(t) orS_(λb)(t), are input to a correlation canceler 27, such as an adaptivenoise canceler 30, an example of which is shown in FIGS. 5a and 5 b anda preferred example of which is discussed herein under the headingPREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATORIMPLEMENTATION. The correlation canceler 27 removes either the secondaryportion n_(λa)(t) or n_(λb)(t), or the primary portions, s_(λa)(t) ors_(λb)(t), of the measured signal yielding a good approximation toeither the primary signals s″_(λa)(t)≈ε_(5,λa) c ₅ x ₅(t) ors″_(λb)(t)≈ε_(5,λb) c ₅ x ₅(t) or the secondary signalsn″_(λa)(t)≈n_(λa)(t) or n″_(λb)(t)≈n_(λb)(t). In the event that theprimary signals are obtained, the concentration c₅(t) may then bedetermined from the approximation to the primary signal s″_(λa)(t) ors″_(λb)(t) according to:

c ₅(t)≈s″ _(λa)(t)/ε_(5,λa) x ₅(t)  (17a)

or

c ₅(t)≈s″ _(λb)(t)/ε_(5,μb) x ₅(t)  (17b)

[0120] As discussed previously, the absorption coefficients are constantat each wavelength λa and λb and the thickness of the primary signalcomponent, x₅(t) in this example, is often known or can be determined asa function of time, thereby allowing calculation of the concentrationc₅(t) of constituent A₅.

Determination of Concentration or Saturation in a Volume Containing Morethan One Constituent

[0121] Referring to FIG. 6b, another material having N differentconstituents arranged in layers is shown. In this material, twoconstituents A₅ and A₆ are found within one layer having thicknessx_(5,6)(t)=x₅(t)+x₆(t), located generally randomly within the layer.This is analogous to combining the layers of constituents A₅ and A₆ inFIG. 6a. A combination of layers, such as the combination of layers ofconstituents A₅ and A₆, is feasible when the two layers are under thesame total forces which result in the same change of the optical pathlengths x₅(t) and x₆(t) of the layers.

[0122] Often it is desirable to find the concentration or thesaturation, i.e., a percent concentration, of one constituent within agiven thickness which contains more than one constituent and is subjectto unique forces. A determination of the concentration or the saturationof a constituent within a given volume may be made with any number ofconstituents in the volume subject to the same total forces andtherefore under the same perturbation or change. To determine thesaturation of one constituent in a volume comprising many constituents,as many measured signals as there are constituents which absorb incidentlight energy are necessary. It will be understood that constituentswhich do not absorb light energy are not consequential in thedetermination of saturation. To determine the concentration, as manysignals as there are constituents which absorb incident light energy arenecessary as well as information about the sum of concentrations.

[0123] It is often the case that a thickness under unique motioncontains only two constituents. For example, it may be desirable to knowthe concentration or saturation of A₅ within a given volume whichcontains A₅ and A₆. In this case, the primary signals s_(λa)(t) ands_(λb)(t) comprise terms related to both A₅ and A₆ so that adetermination of the concentration or saturation of A₅ or A₆ in thevolume may be made. A determination of saturation is discussed herein.It will be understood that the concentration of A₅ in a volumecontaining both A₅ and A₆ could also be determined if it is known thatA₅+A₆=1, i.e., that there are no constituents in the volume which do notabsorb incident light energy at the particular measurement wavelengthschosen. The measured signals S_(λa)(t) and S_(λb)(t) can be written(logarithm converted) as: $\begin{matrix}{{S_{\lambda \quad a}(t)} = {{ɛ_{5,{\lambda \quad a}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \quad a}}c_{6}{x_{5,6}(t)}} + {n_{\lambda \quad a}(t)}}} & \left( {18a} \right) \\{\quad {= {{s_{\lambda \quad a}(t)} + {n_{\lambda \quad a}(t)}}}} & \left( {18b} \right) \\{{S_{\lambda \quad b}(t)} = {{ɛ_{5,{\lambda \quad b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \quad b}}c_{6}{x_{5,6}(t)}} + {n_{\lambda \quad b}(t)}}} & \left( {19a} \right) \\{\quad {= {{s_{\lambda \quad b}(t)} + {{n_{\lambda \quad b}(t)}.}}}} & \left( {19b} \right)\end{matrix}$

[0124] It is also often the case that there may be two or morethicknesses within a medium each containing the same two constituentsbut each experiencing a separate motion as in FIG. 6c. For example, itmay be desirable to know the concentration or saturation of A₅ within agiven volume which contains A₅ and A₆ as well as the concentration orsaturation of A₃ within a given volume which contains A₃ and A₄, A₃ andA₄ having the same constituency as A₅ and A₆ respectively. In this case,the primary signals s_(λa)(t) and s_(λb)(t) again comprise terms relatedto both A₅ and A₆ and portions of the secondary signals n_(λa)(t) andn_(λb)(t) comprise terms related to both A₃ and A₄. The layers, A₃ andA₄, do not enter into the primary equation because they are assumed tobe perturbed by a different frequency, or random or erratic secondaryforces which are uncorrelated with the primary force. Since constituents3 and 5 as well as constituents 4 and 6 are taken to be the same, theyhave the same absorption coefficients (i.e., ε_(3,λa)=ε_(5,λa);ε_(3,λb)=ε_(5,λb); ε_(4,λa)=ε_(6,λa) and ε_(4,λb)=ε_(6,λb). Generallyspeaking, however, A₃ and A₄ will have different concentrations than A₅and A₆ and will therefore have a different saturation. Consequently asingle constituent within a medium may have one or more saturationsassociated with it. The primary and secondary signals according to thismodel may be written as: $\begin{matrix}{{s_{\lambda \quad a}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \quad a}}c_{5}} + {ɛ_{6,{\lambda \quad a}}c_{6}}} \right\rbrack {x_{5,6}(t)}}} & \left( {20a} \right) \\{{n_{\lambda \quad a}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \quad a}}c_{3}} + {ɛ_{6,{\lambda \quad a}}c_{4}}} \right\rbrack {x_{3,4}(t)}} +}} & \quad \\{{\sum\limits_{i = 1}^{2}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}{x_{i}(t)}}} + {\sum\limits_{i = 7}^{n}\quad {\varepsilon_{i,{\lambda \quad a}}c_{i}{x_{i}(t)}}}} & \left( {20b} \right)\end{matrix}$

 n _(λa)(t)=[ε_(5,λa) c ₃+ε_(6,λa) c ₄ ]x _(3,4)(t)+n _(λa)(t)  (20c)$\begin{matrix}{{s_{\lambda \quad b}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \quad b}}c_{5}} + {ɛ_{6,{\lambda \quad b}}c_{6}}} \right\rbrack {x_{5,6}(t)}}} & \left( {21a} \right) \\{{n_{\lambda \quad b}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \quad b}}c_{3}} + {ɛ_{6,{\lambda \quad b}}c_{4}}} \right\rbrack {x_{3,4}(t)}}} & \quad\end{matrix}$

 n _(λb)(t)=[ε_(5,λb) c ₃+ε_(6,λb) c ₄ ]x _(3,4)(t)+n _(λb)(t)  (21c)

[0125] where signals n_(λa)(t) and n_(λb)(t) are similar to thesecondary signals n_(λa)(t) and n_(λb)(t) except for the omission of the3, 4 layer.

[0126] Any signal portions whether primary or secondary, outside of aknown bandwidth of interest, including the constant undesired secondarysignal portion resulting from the generally constant absorption of theconstituents when not under perturbation, should be removed to determinean approximation to either the primary signal or the secondary signalwithin the bandwidth of interest. This is easily accomplished bytraditional band pass filtering techniques. As in the previous example,it is often the case that the total perturbation or change affecting thelayers associated with the secondary signal components is caused byrandom or erratic forces, causing the thickness of each layer, or theoptical path length of each layer, x_(i)(t), to change erratically,producing a random or erratic secondary signal component n_(λa)(t).Regardless of whether or not the secondary signal portion n_(λa)(t) iserratic, the secondary signal component n_(λa)(t) can be removed orderived via a correlation canceler, such as an adaptive noise canceler,having as one input a secondary reference n′(t) or a primary references′(t) determined by a processor of the present invention as long as theperturbation in layers other than the layer of constituents A₅ and A₆ isdifferent than the perturbation in the layer of constituents A₅ and A₆.Either the erratic secondary signal components n_(λa)(t) and n_(λb)(t)or the primary components s_(λa)(t) and s_(λb)(t) may advantageously beremoved from equations (18) and (19), or alternatively equations (20)and (21), by a correlation canceler. The correlation canceler, again,requires a sample of either the primary reference s′(t) or the secondaryreference n′(t) and a sample of either of the composite signalsS_(λa)(t) or S_(λb)(t) of equations (18) and (19).

Determination of Primary and Secondary Reference Signals for SaturationMeasurements

[0127] One method for determining reference signals s′(t) or n′(t) fromthe measured signals S_(λa)(t) and S_(λb)(t) in accordance with oneaspect of the invention is what will be referred to as the constantsaturation approach. In this approach, it is assumed that the saturationof A₅ in the volume containing A₅ and A₆ and the saturation of A₃ in thevolume containing A₃ and A₄ remains relatively constant over some periodof time, i.e.:

Saturation(A ₅(t))=c ₅(t)/[c ₅(t)+c ₆(t)]  (22a)

Saturation(A ₃(t))=c ₃(t)/[c ₃(t)+c ₄(t)]  (22b)

Saturation(A ₅(t))={1+[c ₆(t)/c ₅(t)]}⁻¹  (23a)

Saturation(A ₃(t))={1+[c ₄(t)/c ₃(t)]}⁻¹  (23b)

[0128] are substantially constant over many samples of the measuredsignals Sa and Sxb. This assumption is accurate over many samples sincesaturation generally changes relatively slowly in physiological systems.

[0129] The constant saturation assumption is equivalent to assumingthat:

c ₅(t)/c ₆(t)=constant₁  (24a)

c ₃(t)/c ₄(t)=constant₂  (24b)

[0130] since the only other term in equations (23a) and (23b) is aconstant, namely the numeral 1.

[0131] Using this assumption, the proportionality constants r_(a) andr_(v) which allow determination of the secondary reference signal n′(t)and the primary reference signal s′(t) in the constant saturation methodare: $\begin{matrix}{r_{a} = \frac{{ɛ_{5,{\lambda \quad a}}c_{5 -}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \quad a}}c_{6}{x_{5,6}(t)}}}{{ɛ_{5,{\lambda \quad b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \quad b}}c_{6}{x_{5,6}(t)}}}} & \left( {25a} \right) \\{\quad {= {{s_{\lambda \quad a}(t)}/{s_{\lambda \quad b}(t)}}}} & \left( {26a} \right) \\{\quad {= \frac{{ɛ_{5,{\lambda \quad a}}c_{5}} + {ɛ_{6,{\lambda \quad a}}c_{6}}}{{ɛ_{5,{\lambda \quad b}}c_{5}} + {ɛ_{6,{\lambda \quad b}}c_{6}}}}} & \left( {27a} \right) \\{\quad {= \frac{{ɛ_{5,{\lambda \quad a}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \quad a}}}{{ɛ_{5,{\lambda \quad b}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \quad b}}}}} & \left( {28a} \right) \\{\quad {{{\approx {{s_{\lambda \quad a}^{''}(t)}/{s_{\lambda \quad b}^{''}(t)}}} = {constant}_{3}};{where}}} & \left( {29a} \right) \\{{n_{\lambda \quad a}(t)} \neq {{r_{a}(t)}{n_{\lambda \quad b}(t)}}} & \left( {30a} \right) \\{and} & \quad \\{r_{v} = \frac{{ɛ_{5,{\lambda \quad a}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \quad a}}c_{4}{x_{3,4}(t)}}}{\left. {{ɛ_{5,{\lambda \quad b}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \quad b}}c_{4}{x_{3,4}(t)}}} \right)}} & \left( {25b} \right) \\{\quad {= {{n_{\lambda \quad a}(t)}/{n_{\lambda \quad b}(t)}}}} & \left( {26b} \right) \\{\quad {= \frac{{ɛ_{5,{\lambda \quad a}}c_{3}} + {ɛ_{6,{\lambda \quad a}}c_{4}}}{{ɛ_{5,{\lambda \quad b}}c_{3}} + {ɛ_{6,{\lambda \quad b}}c_{4}}}}} & \left( {27b} \right) \\{\quad {= \frac{{ɛ_{5,{\lambda \quad a}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \quad a}}}{{ɛ_{5,{\lambda \quad b}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \quad b}}}}} & \left( {28b} \right) \\{\quad {{{\approx {{n_{\lambda \quad a}^{''}(t)}/{n_{\lambda \quad b}^{''}(t)}}} = {constant}_{4}};{where}}} & \left( {29b} \right) \\{{s_{\lambda \quad a}(t)} \neq {{r_{v}(t)}{{s_{\lambda \quad b}(t)}.}}} & \left( {30b} \right)\end{matrix}$

[0132] In accordance with the present invention, it is often the casethat both equations (26) and (30) can be simultaneously satisfied todetermine the proportionality constants r_(a) and r_(v). Additionally,the absorption coefficients at each wavelength ε_(5,λa), ε_(6,λa),ε_(5,λb), and ε_(6,λb) are constant and the central assumption of theconstant saturation method is that c₅(t)/c₆(t) and c₃(t)/c₄(t) areconstant over many sample periods. Thus, new proportionality constantsr_(a) and r_(v) may be determined every few samples from newapproximations to either the primary or secondary signal as output fromthe correlation canceler. Thus, the approximations to either the primarysignals s_(λa)(t) and s_(λb)(t) or the secondary signals n_(λa)(t) andn_(λb)(t), found by the correlation canceler for a substantiallyimmediately preceding set of samples of the measured signals S_(λa)(t)and S_(λb)(t) are used in a processor of the present invention forcalculating the proportionality constants, r_(a) and r_(v), for the nextset of samples of the measured signals S_(λa)(t) and S_(λb)(t).

[0133] Multiplying equation (19) by r_(a) and subtracting the resultingequation from equation (18) yields a non-zero secondary referencesignal:

n′(t)=S _(λa)(t)−r _(a) S _(λb)(t)=n _(λa)(t)−r _(a) n _(λb)(t).  (31a)

[0134] Multiplying equation (19) by r_(v) and subtracting the resultingequation from equation (18) yields a non-zero primary reference signal:

s′(t)=S _(λa)(t)−r _(v) S _(λb)(t)=s _(λa)(t)−r _(v) s _(λb)(t).  (31 b)

[0135] When using the constant saturation method in patient monitoring,initial proportionality coefficients can be determined as furtherexplained below. It is not necessary for the patient to remainmotionless even for an initialization period. With values for theproportionality coefficients r_(a) and r_(v) determined, a correlationcanceler may be utilized with a secondary reference n′(t) or a primaryreference s′(t).

Determination of Signal Coefficients for Primary and Secondary ReferenceSignals using the Constant Saturation Method

[0136] In accordance with one aspect of the present invention, thereference processor 26 of FIG. 4a and FIG. 4b of the present inventionmay be configured to multiply the second measured assumed signalS_(λb)(t)=s_(λb)(t)+n_(λb)(t) by each of a plurality of signalcoefficients r₁, r₂, . . . r_(n) and then subtract each result from thefirst measured signal S_(λa)(t)=s_(λa)(t)+n_(λa)(t) to obtain aplurality of reference signals

R′(r, t)=s _(λa)(t)−rs _(λb)(t)+n _(λa)(t)−rn _(λb)(t)  (32)

[0137] for r=r₁, r₂, . . . r_(n) as shown in FIG. 7a. In other words, aplurality of signal coefficients are chosen to represent a cross sectionof possible signal coefficients.

[0138] In order to determine either the primary reference s′(t) or thesecondary reference n′(t) from the above plurality of reference signalsof equation (32), signal coefficients ra and r, are determined from theplurality of assumed signal coefficients r₁, r₂, . . . r_(n). Thecoefficients r_(a) and r_(v) are selected such that they cause eitherthe primary signal portions s_(λa)(t) and s_(λb)(t) or the secondarysignal portions n_(λa)(t) and n_(λb)(t) to cancel or nearly cancel whenthey are substituted into the reference function R′(r, t), e.g.

s _(λa)(t)=r _(a) s _(λb)(t)  (33a)

n _(λa)(t)=r _(v) n _(λb)(t)  (33b)

n′(t)=R′(r _(a) , t)=n _(λa)(t)−r _(a) n _(λb)(t)  (33c)

s′(t)=R′(r _(v) , t)=s _(λa)(t)−r _(v) s _(λb)(t).  (33d)

[0139] In other words, coefficients r_(a) and r_(v) are selected atvalues which reflect the minimum of correlation between the primarysignal portions and the secondary signal portions. In practice, one doesnot usually have significant prior information about either the primarysignal portions s_(λa)(t) and s_(λb)(t) or the secondary signal portionsn_(λa)(t) and n_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t).The lack of this information makes it difficult to determine which ofthe plurality of coefficients r₁, r₂, . . . r_(n) correspond to thesignal coefficients r_(a)=s_(λa)(t)/s_(λb)(t) andr_(v)=n_(λa)(t)/n_(λb)(t).

[0140] One approach to determine the signal coefficients r_(a) and r_(v)from the plurality of coefficients r₁, r₂, . . . r_(n) employs the useof a correlation canceler 27, such as an adaptive noise canceler, whichtakes a first input which corresponds to one of the measured signalsS_(λa)(t) or S_(λb)(t) and takes a second input which corresponds tosuccessively each one of the plurality of reference signals R′(r₁, t),R′(r₂, t), . . . , R′(r_(n), t) as shown in FIG. 7a. For each of thereference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_(n), t) thecorresponding output of the correlation canceler 27 is input to a“squares” operation 28 which squares the output of the correlationcanceler 27. The output of the squares operation 28 is provided to anintegrator 29 for forming a cumulative output signal (a summation of thesquares). The cumulative output signal is subsequently input to anextremum detector 31. The purpose of the extremum detector 31 is tochose signal coefficients r_(a) and r_(v) from the set r₁, r₂, . . .r_(n) by observing which provide a maximum in the cumulative outputsignal as in FIGS. 7b and 7 c. In other words, coefficients whichprovide a maximum integrated output, such as energy or power, from thecorrelation canceler 27 correspond to the signal coefficients r_(a) andr_(v) which relate to a minimum correlation between the primary signalportions and the secondary signal portions in accordance with the signalmodel of the present invention. One could also configure a systemgeometry which would require one to locate the coefficients from the setr₁, r₂, . . . r_(n) which provide a minimum or inflection in thecumulative output signal to identify the signal coefficients r_(a) andr_(v).

[0141] Use of a plurality of coefficients in the processor of thepresent invention in conjunction with a correlation canceler 27 todetermine the signal coefficients r_(a) and r_(v) may be demonstrated byusing the properties of correlation cancellation. If x, y and z aretaken to be any collection of three time varying signals, then theproperties of some correlation cancelers C(x, y) may be defined asfollows:

Property (1) C(x, y)=0 for x, y correlated  (34a)

Property (2) C(x, y)=x for x, y uncorrelated  (34 b)

Property (3) C(x+y, z)=C(x, z)+C(y, z)  (34c)

[0142] With properties (1), (2) and (3) it is easy to demonstrate thatthe energy or power output of a correlation canceler with a first inputwhich corresponds to one of the measured signals S_(λa)(t) or S_(λb)(t)and a second input which corresponds to successively each one of aplurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_(n),t) can determine the signal coefficients r_(a) and r_(v) needed toproduce the primary reference s′(t) and secondary reference n′(t). If wetake as a first input to the correlation canceler the measured signalS_(λa)(t) and as a second input the plurality of reference signalsR′(r₁, t), R′(r₂, t), . . . , R′(r_(n), t) then the outputs of thecorrelation canceler C(S_(λa)(t), R′(r_(j),t)) for j=1, 2, . . . , n maybe written as

C(s _(λa)(t)+n _(λa)(t), s _(λa)(t)−r _(j) s _(λb)(t)+n _(λa)(t)−r _(j)n _(λb)(t))  (35)

[0143] where j=1, 2, . . . , n and we have used the expressions

R′(r, t)=S _(λa)(t)−rS _(λb)(t)  (36)

S _(λa)(t)=s _(λa)(t)+n _(λa)(t)  (37a)

S _(λb)(t)=s _(λb)(t)+n _(λb)(t).  (37b)

[0144] The use of property (3) allows one to expand equation (35) intotwo terms

C(S _(λa)(t), R′(r,t))=C(s _(λa)(t), s _(λa)(t)−rs _(λb)(t)+n_(λa)(t)−rn _(λb)(t))+C(n _(λa)(t), s _(λa)(t)−rs _(λb)(t)+n _(λa)(t)−rn_(λb)(t))  (38)

[0145] so that upon use of properties (1) and (2) the correlationcanceler output is given by

C(S _(λa)(t), R′(r _(j) ,t))=s _(λa)(t)δ(r _(j) −r _(a))+n _(λa)(t)δ(r_(j) −r _(v))  (39)

[0146] where δ(x) is the unit impulse function

δ(x)=0 if x≠0

δ(x)=1 if x=0.  (40)

[0147] The time variable, t, of the correlation canceler outputC(S_(λa)(t), R′(r_(j), t)) may be eliminated by computing its energy orpower. The energy of the correlation canceler output is given by$\begin{matrix}\begin{matrix}{{E_{\lambda \quad a}\left( r_{j} \right)} = {\int{C^{2}\left( {{S_{\lambda \quad a}(t)},{{R^{\prime}\left( {r_{j},t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {r_{j} - r_{a}} \right)}{\int{{s_{\lambda \quad a}^{2}(t)}{t}}}} + {{\delta \left( {r_{j} - r_{v}} \right)}{\int{{n_{\lambda \quad a}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {41a} \right)\end{matrix}$

[0148] It should be understood that one could, equally well, have chosenthe measured signal S_(λb)(t) as the first input to the correlationcanceler and the plurality of reference signals R′(r₁, t), R′(r₂, t), .. . , R′(r_(n), t) as the second input. In this event, the correlationcanceler energy output is $\begin{matrix}\begin{matrix}{{E_{\lambda \quad b}\left( r_{j} \right)} = {\int{C^{2}\left( {{S_{\lambda \quad b}(t)},{{R^{\prime}\left( {r,t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {r_{j} - r_{a}} \right)}{\int{{s_{\lambda \quad b}^{2}(t)}{t}}}} + {{\delta \left( {r_{j} - r_{v}} \right)}{\int{{n_{\lambda \quad b}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {41b} \right)\end{matrix}$

[0149] It should also be understood that in practical situations the useof discrete time measurement signals may be employed as well ascontinuous time measurement signals. A system which performs a discretetransform (e.g., a saturation transform in the present example) inaccordance with the present invention is described with reference toFIGS. 11-22. In the event that discrete time measurement signals areused, integration approximation methods such as the trapezoid rule,midpoint rule, Tick's rule, Simpson's approximation or other techniquesmay be used to compute the correlation canceler energy or power output.In the discrete time measurement signal case, the energy output of thecorrelation canceler may be written, using the trapezoid rule, as$\begin{matrix}\begin{matrix}{{E_{\lambda \quad a}\left( r_{j} \right)} = {{{\delta \left( {r_{j} - r_{a}} \right)}\Delta \quad t\left\{ {{\sum\limits_{i = 0}^{n}\quad {s_{\lambda \quad a}^{2}\left( t_{i} \right)}} - {0.5\left( {{s_{\lambda \quad a}^{2}\left( t_{0} \right)} + {s_{\lambda \quad a}^{2}\left( t_{n} \right)}} \right)}} \right\}} +}} \\{{{\delta \left( {r_{j} - r_{v}} \right)}\Delta \quad t\left\{ {{\sum\limits_{i = 0}^{n}\quad {n_{\lambda \quad a}^{2}\left( t_{i} \right)}} - {0.5\left( {{n_{\lambda \quad a}^{2}\left( t_{0} \right)} + {n_{\lambda \quad a}^{2}\left( t_{n} \right)}} \right)}} \right\}}}\end{matrix} & \left( {42a} \right) \\\begin{matrix}{{E_{\lambda \quad b}(r)} = {{{\delta \left( {r_{j} - r_{a}} \right)}\Delta \quad t\left\{ {{\sum\limits_{i = 0}^{n}\quad {s_{\lambda \quad b}^{2}\left( t_{i} \right)}} - {0.5\left( {{s_{\lambda \quad b}^{2}\left( t_{0} \right)} + {s_{\lambda \quad b}^{2}\left( t_{n} \right)}} \right)}} \right\}} +}} \\{{{\delta \left( {r_{j} - r_{v}} \right)}\Delta \quad t\left\{ {{\sum\limits_{i = 0}^{n}\quad {n_{\lambda \quad b}^{2}\left( t_{i} \right)}} - {0.5\left( {{n_{\lambda \quad b}^{2}\left( t_{0} \right)} + {n_{\lambda \quad b}^{2}\left( t_{n} \right)}} \right)}} \right\}}}\end{matrix} & \left( {42b} \right)\end{matrix}$

[0150] where t_(i) is the i^(th) discrete time, t₀ is the initial time,t_(n) is the final time and Δt is the time between discrete timemeasurement samples.

[0151] The energy functions given above, and shown in FIG. 7b, indicatethat the correlation canceler output is usually zero due to correlationbetween the measured signal S_(λa)(t) or S_(λb)(t) and many of theplurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_(n),t). However, the energy functions are non zero at values of r_(j) whichcorrespond to cancellation of either the primary signal portionss_(λa)(t) and s_(λb)(t) or the secondary signal portions n_(λa)(t) andn_(λb)(t) in the reference signal R′(r_(j), t). These values correspondto the signal coefficients r_(a) and r_(v).

[0152] It should be understood that there may be instances in time wheneither the primary signal portions s_(λa)(t) and s_(λb)(t) or thesecondary signal portions n_(λa)(t) and n_(λb)(t) are identically zeroor nearly zero. In these cases, only one signal coefficient value willprovide maximum energy or power output of the correlation canceler.

[0153] Since there may be more than one signal coefficient value whichprovides maximum correlation canceler energy or power output, anambiguity may arise. It may not be immediately obvious which signalcoefficient together with the reference function R′(r, t) provideseither the primary or secondary reference. In such cases, it isnecessary to consider the constraints of the physical system at hand.For example, in pulse oximetry, it is known that arterial blood, whosesignature is the primary plethysmographic wave, has greater oxygensaturation than various blood, whose signature is the secondary erraticor random signal. Consequently, in pulse oximetry, the ratio of theprimary signals due to arterial pulsation r_(a)=s_(λa)(t)/s_(λb)(t) isthe smaller of the two signal coefficient values while the ratio of thesecondary signals due to mainly venous blood dynamicsr_(v)=n_(λa)(t)/n_(λb)(t) is the larger of the two signal coefficientvalues, assuming λa=660 nm and λb=910 nm.

[0154] It should also be understood that in practical implementations ofthe plurality of reference signals and cross correlator technique, theideal features listed as properties (1), (2) and (3) above will not beprecisely satisfied but will be approximations thereof. Therefore, inpractical implementations of this embodiment of the present invention,the correlation canceler energy curves depicted in FIG. 7b will notconsist of infinitely narrow delta functions but will have finite widthassociated with them as depicted in FIG. 7c.

[0155] It should also be understood that it is possible to have morethan two signal coefficient values which produce maximum energy or poweroutput from a correlation canceler. This situation arises when themeasured signals each contain more than two components each of which arerelated by a ratio as follows: $\begin{matrix}\begin{matrix}{{s_{\lambda \quad a}(t)} = {\sum\limits_{i = 0}^{n}\quad {f_{{\lambda \quad a},i}(t)}}} \\{{s_{\lambda \quad b}(t)} = {\sum\limits_{i = 0}^{n}\quad {f_{{\lambda \quad b},i}(t)}}}\end{matrix} & (43)\end{matrix}$

[0156] where

f _(λa,i)(t)=r _(i) f _(λb,i)(t) i=1, . . . ,n r _(i) ≠r _(j).

[0157] Thus, reference signal techniques together with a correlationcancellation, such as an adaptive noise canceler, can be employed todecompose a signal into two or more signal components each of which isrelated by a ratio.

Preferred Correlation Canceler using a Joint Process EstimatorImplementation

[0158] Once either the secondary reference n′(t) or the primaryreference s′(t) is determined by the processor of the present invention,the correlation canceler can be implemented in either hardware orsoftware. The preferred implementation of a correlation canceler is thatof an adaptive noise canceler using a joint process estimator.

[0159] The least mean squares (LMS) implementation of the internalprocessor 32 described above in conjunction with the adaptive noisecanceler of FIG. 5a and FIG. 5b is relatively easy to implement, butlacks the speed of adaptation desirable for most physiologicalmonitoring applications of the present invention. Thus, a fasterapproach for adaptive noise canceling, called a least-squares latticejoint process estimator model, is used in one embodiment. A jointprocess estimator 60 is shown diagrammatically in FIG. 8 and isdescribed in detail in Chapter 9 of Adaptive Filter Theory by SimonHaykin, published by Prentice-Hall, copyright 1986. This entire book,including Chapter 9, is hereby incorporated herein by reference.

[0160] The function of the joint process estimator is to remove eitherthe secondary signal portions n_(λa)(t) or n_(λb)(t) or the primarysignal portions s_(λa)(t) or s_(λb)(t) from the measured signalsS_(λa)(t) or S_(λb)(t), yielding either a primary signal approximations″_(λa)(t) or s″_(λb)(t) or a secondary signal approximation n″_(λa)(t)or n″_(λb)(t). Thus, the joint process estimator estimates either thevalue of the primary signals s_(λa)(t) or s_(λb)(t) or the secondarysignals n_(λa)(t) or n_(λb)(t). The inputs to the joint processestimator 60 are either the secondary reference n′(t) or the primaryreference s′(t) and the composite measured signal S_(λa)(t) orS_(λb)(t). The output is a good approximation to the signal S_(λa)(t) orS_(λb)(t) with either the secondary signal or the primary signalremoved, i.e. a good approximation to either s_(λa)(t), s_(λb)(t),n_(λa)(t) or n_(λb)(t).

[0161] The joint process estimator 60 of FIG. 8 utilizes, inconjunction, a least square lattice predictor 70 and a regression filter80. Either the secondary reference n′(t) or the primary reference s′(t)is input to the least square lattice predictor 70 while the measuredsignal S_(λa)(t) or S_(λb)(t) is input to the regression filter 80. Forsimplicity in the following description, S_(λa)(t) will be the measuredsignal from which either the primary portion s_(λa)(t) or the secondaryportion n_(λa)(t) will be estimated by the joint process estimator 60.However, it will be noted that S_(λb)(t) could also be input to theregression filter 80 and the primary portion s_(λb)(t) or the secondaryportion n_(λb)(t) of this signal could be estimated.

[0162] The joint process estimator 60 removes all frequencies that arepresent in both the reference n'(t) or s′(t), and the measured signalS_(λa)(t). The secondary signal portion n_(λa)(t) usually comprisesfrequencies unrelated to those of the primary signal portion s_(λa)(t).It is improbable that the secondary signal portion n_(λa)(t) would be ofexactly the same spectral content as the primary signal portions_(λa)(t). However, in the unlikely event that the spectral content ofs_(λa)(t) and n_(λa)(t) are similar, this approach will not yieldaccurate results. Functionally, the joint process estimator 60 comparesthe reference input signal n′(t) or s′(t), which is correlated to eitherthe secondary signal portion n_(λa)(t) or the primary signal portions_(λa)(t), and input signal S_(λa)(t) and removes all frequencies whichare identical. Thus, the joint process estimator 60 acts as a dynamicmultiple notch filter to remove those frequencies in the secondarysignal component n_(λa)(t) as they change erratically with the motion ofthe patient or those frequencies in the primary signal components_(λa)(t) as they change with the arterial pulsation of the patient.This yields a signal having substantially the same spectral content andamplitude as either the primary signal s_(λa)(t) or the secondary signaln_(λa)(t). Thus, the output s″_(λa)(t) or n″_(λa)(t) of the jointprocess estimator 60 is a very good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t).

[0163] The joint process estimator 60 can be divided into stages,beginning with a zero-stage and terminating in an m^(th)-stage, as shownin FIG. 8. Each stage, except for the zero-stage, is identical to everyother stage. The zero-stage is an input stage for the joint processestimator 60. The first stage through the m^(th)-stage work on thesignal produced in the immediately previous stage, i.e., the(m−1)^(th)-stage, such that a good primary signal approximations″_(λa)(t) or secondary signal approximation n″_(λa)(t) is produced asoutput from the m^(th)-stage.

[0164] The least-squares lattice predictor 70 comprises registers 90 and92, summing elements 100 and 102, and delay elements 110. The registers90 and 92 contain multiplicative values of a forward reflectioncoefficient Γ_(f,m)(t) and a backward reflection coefficient δ_(b,m)(t)which multiply the reference signal n′(t) or s′(t) and signals derivedfrom the reference signal n′(t) or s′(t). Each stage of theleast-squares lattice predictor outputs a forward prediction errorf_(m)(t) and a backward prediction error b_(m)(t). The subscript m isindicative of the stage.

[0165] For each set of samples, i.e. one sample of the reference signaln′(t) or s′(t) derived substantially simultaneously with one sample ofthe measured signal S_(λ)(t), the sample of the reference signal n′(t)or s′(t) is input to the least-squares lattice predictor 70. Thezero-stage forward prediction error f₀(t) and the zero-stage backwardprediction error b₀(t) are set equal to the reference signal n′(t) ors′(t). The backward prediction error b₀(t) is delayed by one sampleperiod by the delay element 110 in the first stage of the least-squareslattice predictor 70. Thus, the immediately previous value of thereference n′(t) or s′(t) is used in calculations involving thefirst-stage delay element 110. The zero-stage forward prediction erroris added to the negative of the delayed zero-stage backward predictionerror b₀(t−1) multiplied by the forward reflection coefficient valueΓ_(f,1)(t) register 90 value, to produce a first-stage forwardprediction error f₁(t). Additionally, the zero-stage forward predictionerror f₀(t) is multiplied by the backward reflection coefficientσ_(b,1)(t) register 92 value and added to the delayed zero-stagebackward prediction error b₀(t−1) to produce a first-stage backwardprediction error b₁(t). In each subsequent stage, m, of the least squarelattice predictor 70, the previous forward and backward prediction errorvalues, f_(m−1)(t) and b_(m−1)(t−1), the backward prediction error beingdelayed by one sample period, are used to produce values of the forwardand backward prediction errors for the present stage, f_(m)(t) andb_(m)(t).

[0166] The backward prediction error b_(m)(t) is fed to the concurrentstage, m, of the regression filter 80. There it is input to a register96, which contains a multiplicative regression coefficient valueκ_(m,λa)(t). For example, in the zero-stage of the regression filter 80,the zero-stage backward prediction error b₀(t) is multiplied by thezero-stage regression coefficient κ_(0,λa)(t) register 96 value andsubtracted from the measured value of the signal S_(λa)(t) at a summingelement 106 to produce a first stage estimation error signale_(1,λa)(t). The first-stage estimation error signal e_(1,λa)(t) is afirst approximation to either the primary signal or the secondarysignal. This first-stage estimation error signal e_(1,λa)(t) is input tothe first-stage of the regression filter 80. The first-stage backwardprediction error b₁(t), multiplied by the first-stage regressioncoefficient κ_(1,λa)(t) register 96 value is subtracted from thefirst-stage estimation error signal e_(1,λa)(t) to produce thesecond-stage estimation error e_(2,λa)(t). The second-stage estimationerror signal e_(2,λa)(t) is a second, somewhat better approximation toeither the primary signal s_(λa)(t) or the secondary signal n_(λa)(t).

[0167] The same processes are repeated in the least-squares latticepredictor 70 and the regression filter 80 for each stage until a goodapproximation e_(m,λa)(t), to either the primary signal s_(λa)(t) or thesecondary signal n_(λa)(t) is determined. Each of the signals discussedabove, including the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), the estimation error signal e_(m,λa)(t), isnecessary to calculate the forward reflection coefficient Γ_(f,m)(t),the backward reflection coefficient Γ_(b,m)(t), and the regressioncoefficient κ_(m,λa)(t) register 90, 92, and 96 values in each stage, m.In addition to the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), and the estimation error e_(m,λa)(t) signals,a number of intermediate variables, not shown in FIG. 8 but based on thevalues labeled in FIG. 8, are required to calculate the forwardreflection coefficient Γ_(f,m)(t), the backward reflection coefficientΓ_(b,m)(t), and the regression coefficient κ_(m,λa)(t) register 90,92,and 96 values.

[0168] Intermediate variables include a weighted sum of the forwardprediction error squares ℑ_(m)(t), a weighted sum of the backwardprediction error squares β_(m)(t), a scalar parameter Δ_(m)(t), aconversion factor γ_(m)(t), and another scalar parameter ρ_(m,λa)(t).The weighted sum of the forward prediction errors └_(m)(t) is definedas: m  ( t ) = ∑ i = 1 t     λ t - i   f m  ( i )  2 ; ( 44 )

[0169] where without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. The weighted sum of the backward predictionerrors β_(m)(t) is defined as: $\begin{matrix}{{\beta_{m}(t)} = {\sum\limits_{i = 1}^{t}\quad {\lambda^{t = i}{{b_{m}(i)}}^{2}}}} & (45)\end{matrix}$

[0170] where λ again, without a wavelength identifier, a or b, is aconstant multiplicative value unrelated to wavelength and is typicallyless than or equal to one, i.e., λ≦1. These weighted sum intermediateerror signals can be manipulated such that they are more easily solvedfor, as described in Chapter 9, § 9.3 of the Haykin book referencedabove and defined hereinafter in equations (59) and (60).

Description of the Joint Process Estimator

[0171] The operation of the joint process estimator 60 is as follows.When the joint process estimator 60 is turned on, the initial values ofintermediate variables and signals including the parameter Δ_(m−1)(t),the weighted sum of the forward prediction error signals ℑ_(m−1)(t), theweighted sum of the backward prediction error signals β_(m−1)(t), theparameter ρ_(m,λa)(t), and the zero-stage estimation error e_(0,λa)(t)are initialized, some to zero and some to a small positive number δ:

Δ_(m−1)(0)=0;  (46)

ℑ_(m−1)(0)=δ;  (47)

β_(m−1)(0)=δ;  (48)

ρ_(m,λa)(0)=0;  (49)

e _(0,λa)(t)=S _(λa)(t) for t≧0.  (50)

[0172] After initialization, a simultaneous sample of the measuredsignal S_(λa)(t) or S_(λb)(t) and either the secondary reference n′(t)or the primary reference s′(t) are input to the joint process estimator60, as shown in FIG. 8. The forward and backward prediction errorsignals f₀(t) and b₀(t), and intermediate variables including theweighted sums of the forward and backward error signals ℑ₀(t) and β₀(t),and the conversion factor γ₀(t) are calculated for the zero-stageaccording to:

f ₀(t)=b ₀(t)=n′(t)  (51a)

ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|n′(t)|²  (52a)

γ₀(t−1)=1  (53a)

[0173] if a secondary reference n′(t) is used or according to:

f ₀(t)=b ₀(t)=s′(t)  (51b)

ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|s′(t)|²  (52b)

γ₀(t−1)=1  (53b)

[0174] if a primary reference s′(t) is used where λ again, without awavelength identifier, a or b, is a constant multiplicative valueunrelated to wavelength.

[0175] Forward reflection coefficient Γ_(f,m)(t), backward reflectioncoefficient Γ_(b,m)(t), and regression coefficient κ_(m,λa)(t) register90, 92 and 96 values in each stage thereafter are set according to theoutput of the previous stage. The forward reflection coefficientΓ_(f,1)(t), backward reflection coefficient Γ_(b,1)(t), and regressioncoefficient κ_(1,λa)(t) register 90, 92 and 96 values in the first stageare thus set according to the algorithm using values in the zero-stageof the joint process estimator 60. In each stage, m≧1, intermediatevalues and register values including the parameter Δ_(m−1)(t); theforward reflection coefficient Γ_(f,m)(t) register 90 value; thebackward reflection coefficient Γ_(b,m)(t) register 92 value; theforward and backward error signals f_(m)(t) and b_(m)(t); the weightedsum of squared forward prediction errors ℑ_(f,m)(t), as manipulated in §9.3 of the Haykin book; the weighted sum of squared backward predictionerrors β_(b,m)(t), as manipulated in § 9.3 of the Haykin book; theconversion factor γ_(m)(t); the parameter ρ_(m,λa)(t); the regressioncoefficient κ_(m,λa)(t) register 96 value; and the estimation errore_(m+1λa)(t) value are set according to:

Δ_(m−1)(t)=λΔ_(m−1)(t−1)+{b _(m−1)(t−1)f ^(*)_(m−1)(t)/γ_(m−1)(t−1)}  (54)

Γ_(f,m)(t)=−{Δ_(m−1)(t)/β_(m−1)(t−1)}  (55)

Γ_(b,m)(t)=−{Δ^(*) _(m−1)(t)/ℑ_(m−1)(t)}  (56)

f _(m)(t)=f _(m−1)(t)+Γ^(*) _(f,m)(t)b _(m−1)(t−1)  (57)

b _(m)(t)=b _(m−1)(t−1)+Γ^(*) _(b,m)(t)f _(m−1)(t)  (58)

ℑ_(m)(t)=ℑ_(m−1)(t)−{|Δ_(m−1)(t)|²/β_(m−1)(t−1)}  (59)

β_(m)(t)=β_(m−1)(t−1)−{|Δ_(m−1)(t)|²/ℑ_(m−1)(t)}  (60)

γ_(m)(t−1)=γ_(m−1)(t−1)−{|b_(m−1)(t−1) |²/β_(m−1)(t−1)}  (61)

ρ_(m,λa)(t)−λβ_(m,λa)(t−1)+{b _(m)(t)ε^(*) _(m,λa)(t)/γ_(m)(t)}  (62)

κ_(m,λa)(t)={β_(m,λa)(t)/β_(m)(t)}  (63)

ε_(m+1,λa)(t)=ε_(m,λa)(t)−κ^(*) _(m)(t)b _(m)(t)  (64)

[0176] where a (*) denotes a complex conjugate.

[0177] These equations cause the error signals f_(m)(t), b_(m)(t),e_(m,λa)(t) to be squared or to be multiplied by one another, in effectsquaring the errors, and creating new intermediate error values, such asΔ_(m−1)(t). The error signals and the intermediate error values arerecursively tied together, as shown in the above equations (54) through(64). They interact to minimize the error signals in the next stage.

[0178] After a good approximation to either the primary signal s_(λa)(t)or the secondary signal n_(λa)(t) has been determined by the jointprocess estimator 60, a next set of samples, including a sample of themeasured signal S_(λa)(t) and a sample of either the secondary referencen′(t) or the primary reference s′(t), are input to the joint processestimator 60. The re-initialization process does not re-occur, such thatthe forward and backward reflection coefficient Γ_(f,m)(t) andΓ_(b,m)(t) register 90, 92 values and the regression coefficientκ_(m,λa)(t) register 96 value reflect the multiplicative values requiredto estimate either the primary signal portion s_(λa)(t) or the secondarysignal portion n_(λa)(t) of the sample of S_(λa)(t) input previously.Thus, information from previous samples is used to estimate either theprimary or secondary signal portion of a present set of samples in eachstage.

[0179] In a more numerically stable and preferred embodiment of theabove described joint process estimator, a normalized joint processestimator is used. This version of the joint process estimatornormalizes several variables of the above-described joint processestimator such that the normalized variables fall between −1 and 1. Thederivation of the normalized joint process estimator is motivated in theHaykin text as problem 12 on page 640 by redefining the variablesdefined according to the following conditions: f _ m  ( t ) = f m  ( t) m  ( t )  γ m  ( t - 1 ) b _  ( t ) = b m  ( t ) β m  ( t )  γm  ( t ) Δ _ m  ( t ) = Δ m  ( t ) m  ( t )  β m  ( t - 1 )

[0180] This transformation allows the conversion of Equations (54)-(64)to the following normalized equations:

{overscore (Δ)}_(m−1)(t)={overscore (Δ)}_(m−1)(t−1)[1−|f_(m−1)(t)|²]^(1/2)[1|{overscore (b)} _(m−1)(t−1)|²]^(1/2) +{overscore(b)} _(m−1)(t−1){overscore (f)}_(m−1)(t) $\begin{matrix}{{{\overset{\_}{b}}_{m}(t)} = \frac{\left\lbrack {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)} - {{{\overset{\_}{\Delta}}_{m - 1}(t)}{{\overset{\_}{f}}_{m - 1}(t)}}} \right\rbrack}{{\left\lbrack {1 - {{{\overset{\_}{\Delta}}_{m - 1}(t)}}^{2}} \right\rbrack^{1/2}\left\lbrack {1 - {{{\overset{\_}{f}}_{m - 1}(t)}}^{2}} \right\rbrack}^{1/2}}} \\{{{\overset{\_}{f}}_{m}(t)} = \frac{\left\lbrack {{{\overset{\_}{f}}_{m - 1}(t)} - {{{\overset{\_}{\Delta}}_{m - 1}(t)}{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}}} \right\rbrack}{{\left\lbrack {1 - {{{\overset{\_}{\Delta}}_{m - 1}(t)}}^{2}} \right\rbrack^{1/2}\left\lbrack {1 - {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}}^{2}} \right\rbrack}^{1/2}}}\end{matrix}$

 β_(m)(t)=[1−|{overscore (Δ)}_(m−1)(t)|²]β_(m−1)(t− 1)

γ_(m)(t)=γ_(m−1)(t)[1−|{overscore (b)} _(m−1)(t)|²]${\rho_{m}(t)} = {{{\lambda \cdot \left\lbrack \frac{{\gamma_{m}(t)}{\beta_{m}\left( {t - 1} \right)}}{{\gamma_{m}\left( {t - 1} \right)}{\beta_{m}(t)}} \right\rbrack^{\frac{1}{2}}}{\rho_{m}\left( {t - 1} \right)}} + {{{\overset{\_}{b}}_{m}(t)}{ɛ_{m}(t)}}}$

 ε_(m+1,λa)(t)=δ_(m,λa)(t)−ρ_(m)(t){overscore (b)}_(m)(t)

[0181] Initialization of Normalized Joint Process Estimator

[0182] Let N(t) be defined as the reference noise input at time index nand U(t) be defined as combined signal plus noise input at time index tthe following equations apply (see Haykin, p. 619):

[0183] 1. To initialize the algorithm, at time t=0 set

{overscore (Δ)}_(m−1)(0)=0

β_(m−1)(0)=δ=10⁻⁶

γ₀(0)=1

[0184] 2. At each instant t≧1, generate the various zeroth-ordervariables as follows:

γ₀((t−1)=1

β₀(t)=λβ₀(t−1)+N ²(t)${{\overset{\_}{b}}_{0}(t)} = {{{\overset{\_}{f}}_{0}(t)} = \frac{N(t)}{\sqrt{\beta_{0}(t)}}}$

[0185] 3. For regression filtering, initialize the algorithm by settingat time index t=0

ρ_(m)(0)=0

[0186] 4. At each instant t≧1, generate the zeroth-order variable

ε₀(t)=U(t).

[0187] Accordingly, a normalized joint process estimator can be used fora more stable system.

[0188] In yet another embodiment, the correlation cancellation isperformed with a QRD algorithm as shown diagrammatically in FIG. 8a andas described in detail in Chapter 18 of Adaptive Filter Theory by SimonHaykin, published by Prentice-Hall, copyright 1986.

[0189] The following equations adapted from the Haykin book correspondto the QRD-LSL diagram of FIG. 8a (also adapted from the Haykin book).

[0190] Computations

[0191] a. Predictions: For time t=1, 2, . . . , and prediction orderm=1, 2, . . . , M, where M is the final prediction order, compute:

β_(m−1)(t−1)=λβ_(m−1)(t−2)+|ε_(b,m−1)(t−1)|²${c_{b,{m - 1}}\left( {t + 1} \right)} = \frac{\lambda^{1/2}{\beta_{m - 1}^{1/2}\left( {t - 2} \right)}}{\beta_{m - 1}^{1/2}\left( {t - 1} \right)}$${s_{b,{m - 1}}\left( {t - 1} \right)} = \frac{ɛ_{b,{m - 1}}^{*}\left( {t - 1} \right)}{\beta_{m - 1}^{1/2}\left( {t - 1} \right)}$

 ε_(f,m)(t)=c_(b,m−1)(t− 1)ε_(f,m−1)(t)−s^(*) _(b,m−1)(t− 1)λ^(1/2)π^(*)_(f,m−1)(t− 1)

π^(*) _(f,m−1)(t)=c _(b,m−1)(t−1)λ^(1/2)π^(*) _(f,m−1)(t−1)+s_(b,m−1)(t−1)ε_(f,m−1)(t)

γ_(m) ^(1/2)(t−1)=c_(b,m−1)(t−1)γ_(m−1) ^(1/2)(t−1)

ℑ_(m−1)(t)=λ∈_(m−1)(t−1)+|ε_(f,m−1)(t)|² c f , m - 1  ( t ) = λ 1 / 2 m - 1 1 / 2  ( t - 1 ) m - 1 1 / 2  ( t ) s f , m - 1  ( t ) = ɛ f ,m - 1 •  ( t ) m - 1 1 / 2  ( t )

 ε_(b,m)(t)=c_(f,m−1)(t)ε_(b,m−1)(t− 1)−s ^(*) _(f,m−1)(t)λ^(1/2)π^(*)_(b,m−1)(t− 1)

π^(*) _(b,m−1)(t)=c_(f,m−1)(t)λ_(1/2)π^(*) _(b,m−1)(t−1)+s_(f,m−1)(t)ε_(b,m−1)(t−1)

[0192] b. Filtering: For order m=0, 1, . . . , M−1; and time t=1, 2, . .. , compute

β_(m)(t)=λβ_(m)(t−1)+|ε_(b,m)(t)|²${c_{b,m}(t)} = \frac{\lambda^{1/2}{\beta_{m}^{1/2}\left( {t - 1} \right)}}{\beta_{m}^{1/2}(t)}$${s_{b,m}(t)} = \frac{ɛ_{b,m}^{\bullet}(t)}{\beta_{m}^{1/2}(t)}$

 ε_(m+1)(t)=c _(b,m)(t)ε_(m)(t)−s ^(*) _(b,m)(t)λ^(1/2)ρ^(*) _(m)(t− 1)

ρ^(*) _(m)(t)=c _(b,m)(t)λ^(1/2)ρ^(*) _(m)(t−1)+s_(b,m)(t)ε_(m)(t)

γ_(m+1) ^(1/2)(t)=c_(b,m)(t)γ_(m) ^(1/2)(t)

ε_(m+1)(t)=λ_(m+1) ^(1/2)(t)ε_(m+1)(t)

[0193] 5. Initialization

[0194] a. Auxiliary parameter initialization: for order m=1, 2, . . . ,M, set

π_(f,m−1)(0)=π_(b,m−1)(0)=0

p _(m)(0)=0

[0195] b. Soft constraint initialization: For order m=0, 1, . . . , M,set

β_(m)(−1)=δ

ℑ_(m)(0)=δ

[0196] where δ is a small positive constant.

[0197] c. Data initialization: For t=1, 2, . . . , compute

ε_(f,0)(t)=ε_(b,0)(t)=μ(t)

ε₀(t)=d(t)

γ₀(t)=1

[0198] where μ(t) is the input and d(t) is the desired response at timet.

Flowchart of Joint Process Estimator

[0199] In a signal processor, such as a physiological monitorincorporating a reference processor of the present invention todetermine a reference n′(t) or s′(t) for input to a correlationcanceler, a joint process estimator 60 type adaptive noise canceler isgenerally implemented via a software program having an iterative loop.One iteration of the loop is analogous to a single stage of the jointprocess estimator as shown in FIG. 8. Thus, if a loop is iterated mtimes, it is equivalent to an m stage joint process estimator 60.

[0200] A flow chart of a subroutine to estimate the primary signalportion s_(λa)(t) or the secondary signal portion n_(λa)(t) of ameasured composite signal, S_(λa)(t) is shown in FIG. 9. The flow chartillustrates the function of a reference processor for determining eitherthe secondary reference n′(t) or the primary reference s′(t). Theflowchart for the joint process estimator is implemented in software.

[0201] A one-time initialization is performed when the physiologicalmonitor is powered-on, as indicated by an “INITIALIZE NOISE CANCELER”action block 120. The initialization sets all registers 90, 92, and 96and delay element variables 110 to the values described above inequations (46) thrmiioh (50)

[0202] Next, a set of simultaneous samples of the composite measuredsignals S_(λa)(t) and S_(λb)(t) is input to the subroutine representedby the flowchart in FIG. 9. Then a time update of each of the delayelement program variables occurs, as indicated in a “TIME UPDATE OF[Z⁻¹] ELEMENTS” action block 130. The value stored in each of the delayelement variables 110 is set to the value at the input of the delayelement variable 110. Thus, the zero-stage backward prediction errorb₀(t) is stored as the first-stage delay element variable, and thefirst-stage backward prediction error b₁(t) is stored as thesecond-stage delay element variable, and so on.

[0203] Then, using the set of measured signal samples S_(λa)(t) andS_(λb)(t), the reference signal is obtained using the ratiometric or theconstant saturation methods described above. This is indicated by a“CALCULATE REFERENCE [n′(t) or s′(t)] FOR TWO MEASURED SIGNAL SAMPLES”action block 140.

[0204] A zero-stage order update is performed next as indicated in a“ZERO-STAGE UPDATE” action block 150. The zero-stage backward predictionerror b₀(t), and the zero-stage forward prediction error f₀(t) are setequal to the value of the reference signal n′(t) or s′(t). Additionally,the weighted sum of the forward prediction errors ℑ_(m)(t) and theweighted sum of backward prediction errors β_(m)(t) are set equal to thevalue defined in equations (47) and (48).

[0205] Next, a loop counter, m, is initialized as indicated in a “m=0”action block 160. A maximum value of m, defining the total number ofstages to be used by the subroutine corresponding to the flowchart inFIG. 9, is also defined. Typically, the loop is constructed such that itstops iterating once a criterion for convergence upon a bestapproximation to either the primary signal or the secondary signal hasbeen met by the joint process estimator 60. Additionally, a maximumnumber of loop iterations may be chosen at which the loop stopsiteration. In a preferred embodiment of a physiological monitor of thepresent invention, a maximum number of iterations, m=6 to m=10, isadvantageously chosen.

[0206] Within the loop, the forward and backward reflection coefficientΓ_(f,m)(t) and Γ_(b,m)(t) register 90 and 92 values in the least-squareslattice filter are calculated first, as indicated by the “ORDER UPDATEMTH CELL OF LSL-LATTICE” action block 170 in FIG. 9. This requirescalculation of intermediate variable and signal values used indetermining register 90, 92, and 96 values in the present stage, thenext stage, and in the regression filter 80.

[0207] The calculation of regression filter register 96 valueκ_(m,λa)(t) is performed next, indicated by the “ORDER UPDATE MTH STAGEOF REGRESSION FILTER(S)” action block 180. The two order update actionblocks 170 and 180 are performed in sequence m times, until m hasreached its predetermined maximum (in the preferred embodiment, m=6 tom=10) or a solution has been converged upon, as indicated by a YES pathfrom a “DONE” decision block 190. In a computer subroutine, convergenceis determined by checking if the weighted sums of the forward andbackward prediction errors ℑ_(m)(t) and β_(m)(t) are less than a smallpositive number. An output is calculated next, as indicated by a“CALCULATE OUTPUT” action block 200. The output is a good approximationto either the primary signal or secondary signal, as determined by thereference processor 26 and joint process estimator 60 subroutinecorresponding to the flow chart of FIG. 9. This is displayed (or used ina calculation in another subroutine), as indicated by a “TO DISPLAY”action block 210.

[0208] A new set of samples of the two measured signals S_(λa)(t) andS_(λb)(t) is input to the processor and joint process estimator 60adaptive noise canceler subroutine corresponding to the flowchart ofFIG. 9 and the process reiterates for these samples. Note, however, thatthe initialization process does not re-occur. New sets of measuredsignal samples S_(λa)(t) and S_(λb)(t) are continuously input to thereference processor 26 and joint process estimator adaptive noisecanceler subroutine. The output forms a chain of samples which isrepresentative of a continuous wave. This waveform is a goodapproximation to either the primary signal waveform s_(λa)(t) or thesecondary waveform n_(λa)(t) at wavelength λa. The waveform may also bea good approximation to either the primary signal waveform s_(λb)(t) orthe secondary waveform n″_(λb)(t) at wavelength λb.

[0209] A corresponding flowchart for the QRD algorithm of FIG. 8a isdepicted in FIG. 9a, with reference numeral corresponding in number withan ‘a’ extension

Calculation of Saturation from Correlation Canceler Output

[0210] Physiological monitors may use the approximation of the primarysignals s″_(λa)(t) or s″_(λb)(t) or the secondary signals n″_(λa)(t) orn″_(λb)(t) to calculate another quality, such as the saturation of oneconstituent in a volume containing that constituent plus one or moreother constituents. Generally, such calculations require informationabout either a primary or secondary signal at two wavelengths. Forexample, the constant saturation method requires a good approximation ofthe primary signal portions S_(λa)(t) and S_(λb)(t) of both measuredsignals S_(λa)(t) and S_(λb)(t). The arterial saturation is determinedfrom the approximations to both signals, i.e. s″_(λa)(t) and s″_(λb)(t).The constant saturation method also requires a good approximation of thesecondary signal portions n_(λa)(t) or n_(λb)(t). An estimate of thevenous saturation may be determined from the approximations to thesesignals i.e. n″_(λa)(t) and n″_(λb)(t)

[0211] A joint process estimator 60 having two regression filters 80 aand 80 b is shown in FIG. 10. A first regression filter 80 a accepts ameasured signal S_(λa)(t). A second regression filter 80 b accepts ameasured signal S_(λb)(t) for a use of the constant saturation method todetermine the reference signal n′(t) or s′(t). The first and secondregression filters 80 a and 80 b are independent. The backwardprediction error b_(m)(t) is input to each regression filter 80 a and 80b, the input for the second regression filter 80 b bypassing the firstregression filter 80 a.

[0212] The second regression filter 80 b comprises registers 98, andsumming elements 108 arranged similarly to those in the first regressionfilter 80 a. The second regression filter 80 b operates via anadditional intermediate variable in conjunction with those defined byequations (54) through (64), i.e.:

ρ_(m,λb)(t)=λρ_(m,λb)(t−1)+{b _(m)(t)e ^(*) _(m,λb)(t)/γ_(m)(t)};and  (65)

ρ_(0,λb)(0)=0.  (66)

[0213] The second regression filter 80 b has an error signal valuedefined similar to the first regression filter error signal values,e_(m,λa)(t), i.e.:

e _(m+1,λb)(t)=e _(m,λb)(t)−κ^(*) _(m,λb)(t)b _(m)(t); and  (67)

e _(0,λb)(t)=S _(λb)(t) for t≧0.  (68)

[0214] The second regression filter has a regression coefficientκ_(m,λb)(t) register 98 value defined similarly to the first regressionfilter error signal values, i.e.:

κ_(m,λb)(t)={ρ_(m,λb)(t)/β_(m)(t)}; or  (69)

[0215] These values are used in conjunction with those intermediatevariable values, signal values, register and register values defined inequations (46) through (64). These signals are calculated in an orderdefined by placing the additional signals immediately adjacent a similarsignal for the wavelength a.

[0216] For the constant saturation method, S_(λb)(t) is input to thesecond regression filter 80 b. The output is then a good approximationto the primary signal s″_(λb)(t) or secondary signal s″_(λb)(t).

[0217] The addition of the second regression filter 80 b does notsubstantially change the computer program subroutine represented by theflowchart of FIG. 9. Instead of an order update of the m^(th) stage ofonly one regression filter, an order update of the m^(th) stage of bothregression filters 80 a and 80 b is performed. This is characterized bythe plural designation in the “ORDER UPDATE OF m^(th) STAGE OFREGRESSION FILTER(S)” activity block 180 in FIG. 9. Since the regressionfilters 80 a and 80 b operate independently, independent calculationscan be performed in the reference processor and joint process estimator60 adaptive noise canceler subroutine modeled by the flowchart of FIG.9.

[0218] An alternative diagram for the joint process estimator of FIG.10, using the QRD algorithm and having two regression filters is shownin FIG. 10a. This type of joint process estimator would be used forcorrelation cancellation using the QRD algorithm described in the Haykinbook.

Calculation of Saturation

[0219] Once good approximations to the primary signal portionss″_(λa)(t) and s″_(λb)(t) or the secondary signal portion, n″_(λa)(t)and n″_(λb)(t), have been determined by the joint process estimator 60,the saturation of A₅ in a volume containing A₅ and A₆, for example, maybe calculated according to various known methods. Mathematically, theapproximations to the primary signals can be written in terms of a andb, as:

s″ _(λa)(t)≈ε_(5,λa) c ₅ x _(5,6)(t)+ε_(6,λa) c ₆ x _(5,6)(t); and  (70)

s″ _(λb)(t)≈ε_(5,λb) c ₅ x _(5,6)(t)+ε_(6,λb) c ₆ x _(5,6)(t)  (71)

[0220] Equations (70) and (71) are equivalent to two equations havingthree unknowns, namely c₅(t), c₆(t) and x_(5,6)(t). The saturation canbe determined by acquiring approximations to the primary or secondarysignal portions at two different, yet proximate times t₁ and t₂ overwhich the saturation of A₅ in the volume containing A₅ and A₆ and thesaturation of A₃ in the volume containing A₃ and A₄ does not changesubstantially. For example, for the primary signals estimated at timest₁ and t₂:

s″ _(λa)(t _(l))≈ε_(5,λa) c ₅ x _(5,6)(t ₁)+ε_(6,λa) c ₆ x _(5,6)(t₁)  (72)

s″ _(λb)(t ₁)≈ε_(5,λb) c ₅ x _(5,6)(t ₁)+ε_(6,λb) c ₆ x _(5,6)(t₁)  (73)

s″_(λa)(t ₂)≈ε_(5,λa) c ₅ x _(5,6)(t ₂)+ε_(6,λa) c ₆ x _(5,6)(t ₂)  (74)

s″ _(λb)(t ₂)≈ε_(5,λb) c ₅ x _(5,6)(t ₂)+ε_(6,λb) c ₆ x _(5,6)(t₂)  (75)

[0221] Then, difference signals may be determined which relate thesignals of equations (72) through (75), i.e.:

Δs _(λa) =s″ _(λa)(t ₁)−s″ _(λa)(t ₂)≈ε_(5,λa) c ₅ Δx+ε _(,λa) c ₆ Δx;and  (76)

Δs _(λb) =s″ _(λb)(t ₁)−s″ _(λb)(t ₂)≈ε_(5,λb) c ₅ Δx+ε _(,λb) c ₆Δx;  (77)

[0222] where Δx=x_(5,6)(t₁)-x_(5,6)(t₂). The average saturation at timet=(t₁+t₂)/2 is: $\begin{matrix}{{{Saturation}\quad (t)} = {{c_{5}(t)}/\left\lbrack {{c_{5}(t)} + {c_{6}(t)}} \right\rbrack}} & (78) \\{\quad {= \frac{ɛ_{6,{\lambda \quad a}} - {ɛ_{6,{\lambda \quad b}}\left( {\Delta \quad {s_{\lambda \quad a}/\Delta}\quad s_{\lambda \quad b}} \right)}}{ɛ_{6,{\lambda \quad a}} - {{ɛ_{5,{\lambda \quad a}}\left( {ɛ_{6,{\lambda \quad b}} - ɛ_{5,{\lambda \quad b}}} \right)}\left( {\Delta \quad {s_{\lambda \quad a}/\Delta}\quad s_{\lambda \quad b}} \right)}}}} & (79)\end{matrix}$

[0223] It will be understood that the Δx term drops out from thesaturation calculation because of the division. Thus, knowledge of thethickness of the primary constituents is not required to calculatesaturation.

Pulse Oximetry Measurements

[0224] A specific example of a physiological monitor utilizing aprocessor of the present invention to determine a secondary referencen′(t) for input to a correlation canceler that removes erraticmotion-induced secondary signal portions is a pulse oximeter. Pulseoximetry may also be performed utilizing a processor of the presentinvention to determine a primary signal reference s′(t) which may beused for display purposes or for input to a correlation canceler toderive information about patient movement and venous blood oxygensaturation.

[0225] A pulse oximeter typically causes energy to propagate through amedium where blood flows close to the surface for example, an ear lobe,or a digit such as a finger, a forehead or a fetus' scalp. An attenuatedsignal is measured after propagation through or reflected from themedium. The pulse oximeter estimates the saturation of oxygenated blood.

[0226] Freshly oxygenated blood is pumped at high pressure from theheart into the arteries for use by the body. The volume of blood in thearteries varies with the heartbeat, giving rise to a variation inabsorption of energy at the rate of the heartbeat, or the pulse.

[0227] Oxygen depleted, or deoxygenated, blood is returned to the heartby the veins along with unused oxygenated blood. The volume of blood inthe veins varies with the rate of breathing, which is typically muchslower than the heartbeat. Thus, when there is no motion inducedvariation in the thickness of the veins, venous blood causes a lowfrequency variation in absorption of energy. When there is motioninduced variation in the thickness of the veins, the low frequencyvariation in absorption is coupled with the erratic variation inabsorption due to motion artifact.

[0228] In absorption measurements using the transmission of energythrough a medium, two light emitting diodes (LED's) are positioned onone side of a portion of the body where blood flows close to thesurface, such as a finger, and a photodetector is positioned on theopposite side of the finger. Typically, in pulse oximetry measurements,one LED emits a visible wavelength, preferably red, and the other LEDemits an infrared wavelength. However, one skilled in the art willrealize that other wavelength combinations could be used. The fingercomprises skin, tissue, muscle, both arterial blood and venous blood,fat, etc., each of which absorbs light energy differently due todifferent absorption coefficients, different concentrations, differentthicknesses, and changing optical pathlengths. When the patient is notmoving, absorption is substantially constant except for the flow ofblood. The constant attenuation can be determined and subtracted fromthe signal via traditional filtering techniques. When the patient moves,this causes perturbation such as changing optical pathlength due tomovement of background fluids (e.g., venous blood having a differentsaturation than the arterial blood). Therefore, the measured signalbecomes erratic. Erratic motion induced noise typically cannot bepredetermined and/or subtracted from the measured signal via traditionalfiltering techniques. Thus, determining the oxygen saturation ofarterial blood and venous blood becomes more difficult.

[0229] A schematic of a physiological monitor for pulse oximetry isshown in FIGS. 11-13. FIG. 11 depicts a general hardware block diagramof a pulse oximeter 299. A sensor 300 has two light emitters 301 and 302such as LED's. One LED 301 emitting light of red wavelengths and anotherLED 302 emitting light of infrared wavelengths are placed adjacent afinger 310. A photodetector 320, which produces an electrical signalcorresponding to the attenuated visible and infrared light energysignals is located opposite the LED's 301 and 302. The photodetector 320is connected to front end analog signal conditioning circuity 330.

[0230] The front end analog signal conditioning circuitry 330 hasoutputs coupled to analog to digital conversion circuit 332. The analogto digital conversion circuitry 332 has outputs coupled to a digitalsignal processing system 334. The digital signal processing system 334provides the desired parameters as outputs for a display 336. Outputsfor display are, for example, blood oxygen saturation, heart rate, and aclean plethysmographic waveform.

[0231] The signal processing system also provides an emitter currentcontrol output 337 to a digital-to-analog converter circuit 338 whichprovides control information for light emitter drivers 340. The lightemitter drivers 340 couple to the light emitters 301, 302. The digitalsignal processing system 334 also provides a gain control output 342 forthe front end analog signal conditioning circuitry 330.

[0232]FIG. 11a illustrates a preferred embodiment for the combination ofthe emitter drivers 340 and the digital to analog conversion circuit338. As depicted in FIG. 11a, the driver comprises first and secondinput latches 321, 322, a synchronizing latch 323, a voltage reference324, a digital to analog conversion circuit 325, first and second switchbanks 326, 327, first and second voltage to current converters 328, 329and the LED emitters 301, 302 corresponding to the LED emitters 301, 302of FIG. 11.

[0233] The preferred driver depicted in FIG. 11a is advantageous in thatthe present inventors recognized that much of the noise in the oximeter299 of FIG. 11 is caused by the LED emitters 301, 302. Therefore, theemitter driver circuit of FIG. 11a is designed to minimize the noisefrom the emitters 301, 302. The first and second input latches 321, 324are connected directly to the DSP bus. Therefore, these latchessignificantly minimizes the bandwidth (resulting in noise) present onthe DSP bus which passes through to the driver circuitry of FIG. 11a.The output of the first and second input latches only changes when theselatched detect their address on the DSP bus. The first input latchreceives the setting for the digital to analog converter circuit 325.The second input latch receives switching control data for the switchbanks 326, 327. The synchronizing latch accepts the synchronizing pulseswhich maintain synchronization between the activation of emitters 301,302 and the analog to digital conversion circuit 332.

[0234] The voltage reference is also chosen as a low noise DC voltagereference for the digital to analog conversion circuit 325. In addition,in the present embodiment, the voltage reference has an lowpass outputfilter with a very low corner frequency (e.g., 1 Hz in the presentembodiment). The digital to analog converter 325 also has a lowpassfilter at its output with a very low corner frequency (e.g., 1 Hz). Thedigital to analog converter provides signals for each of the emitters301, 302.

[0235] In the present embodiment, the output of the voltage to currentconverters 328, 329 are switched such that with the emitters 301, 302connected in back-to-back configuration, only one emitter is active anany given time. In addition, the voltage to current converter for theinactive emitter is switched off at its input as well, such that it iscompletely deactivated. This reduces noise from the switching andvoltage to current conversion circuitry. In the present embodiment, lownoise voltage to current converters are selected (e.g., Op 270 p Amps),and the feedback loop is configured to have a low pass filter to reducenoise. In the present embodiment, the low pass filtering function of thevoltage to current converter 328, 329 has a corner frequency of justabove 625 Hz, which is the switching speed for the emitters, as furtherdiscussed below. Accordingly, the preferred driver circuit of FIG. 11a,minimizes the noise of the emitters 301, 302.

[0236] In general, the red and infrared light emitters 301, 302 eachemits energy which is absorbed by the finger 310 and received by thephotodetector 320. The photodetector 320 produces an electrical signalwhich corresponds to the intensity of the light energy striking thephotodetector 320. The front end analog signal conditioning circuitry330 receives the intensity signals and filters and conditions thesesignals as further described below for further processing. The resultantsignals are provided to the analog-to-digital conversion circuitry 332which converts the analog signals to digital signals for furtherprocessing by the digital signal processing system 334. The digitalsignal processing system 334 utilizes the two signals in order toprovide a what will be called herein a “saturation transform.” It shouldhe understood, that for parameters other than blood saturationmonitoring, the saturation transform could be better termed as aconcentration transform, in-vivo transform, or the like, depending onthe desired parameter. The term saturation transform is used to describean operation which converts the sample data from time domain tosaturation domain values as will be apparent from the discussion below.In the present embodiment, the output of the digital signal processingsystem 334 provides clean plethysmographic waveforms of the detectedsignals and provides values for oxygen saturation and pulse rate to thedisplay 336.

[0237] It should be understood that in different embodiments of thepresent invention, one or more of the outputs may be provided. Thedigital signal processing system 334 also provides control for drivingthe light emitters 301, 302 with an emitter current control signal onthe emitter current control output 337. This value is a digital valuewhich is converted by the digital-to-analog conversion circuit 338 whichprovides a control signal to the emitter current drivers 340. Theemitter current drivers 340 provide the appropriate current drive forthe red emitter 301 and the infrared emitter 302. Further detail of theoperation of the physiological monitor for pulse oximetry is explainedbelow. In the present embodiment, the light emitters are driven via theemitter current driver 340 to provide light transmission with digitalmodulation at 625 Hz. In the present embodiment, the light emitters 301,302 are driven at a power level which provides an acceptable intensityfor detection by the detector and for conditioning by the front endanalog signal conditioning circuitry 330. Once this energy level isdetermined for a given patient by the digital signal processing system334, the current level for the red and infrared emitters is maintainedconstant. It should be understood, however, that the current could beadjusted for changes in the ambient room light and other changes whichwould effect the voltage input to the front end analog signalconditioning circuitry 330. In the present invention, the red andinfrared light emitters are modulated as follows: for one complete 625Hz red cycle, the red emitter 301 is activated for the first quartercycle, and off for the remaining three-quarters cycle; for one complete625 Hz infrared cycle, the infrared light emitter 302 is activated forone quarter cycle and is off for the remaining three-quarters cycle. Inorder to only receive one signal at a time, the emitters are cycled onand off alternatively, in sequence, with each only active for a quartercycle per 625 Hz cycle and a quarter cycle separating the active times.

[0238] The light signal is attenuated (amplitude modulated) by thepumping of blood through the finger 310 (or other sample medium). Theattenuated (amplitude modulated) signal is detected by the photodetector320 at the 625 Hz carrier frequency for the red and infrared light.Because only a single photodetector is used, the photodetector 320receives both the red and infrared signals to form a composite timedivision signal.

[0239] The composite time division signal is provided to the frontanalog signal conditioning circuitry 330. Additional detail regardingthe front end analog signal conditioning circuitry 330 and the analog todigital converter circuit 332 is illustrated in FIG. 12. As depicted inFIG. 12, the front end circuity 302 has a preamplifier 342, a high passfilter 344, an amplifier 346, a programmable gain amplifier 348, and alow pass filter 350. The preamplifier 342 is a transimpedance amplifierthat converts the composite current signal from the photodetector 320 toa corresponding voltage signal, and amplifies the signal. In the presentembodiment, the preamplifier has a predetermined gain to boost thesignal amplitude for ease of processing. In the present embodiment, thesource voltages for the preamplifier 342 are −15 VDC and +15 VDC. Aswill be understood, the attenuated signal contains a componentrepresenting ambient light as well as the component representing theinfrared or the red light as the case may be in time. If there is lightin the vicinity of the sensor 300 other than the red and infrared light,this ambient light is detected by the photodetector 320. Accordingly,the gain of the preamplifier is selected in order to prevent the ambientlight in the signal from saturating the preamplifier under normal andreasonable operating conditions.

[0240] In the present embodiment, the preamplifier 342 comprises anAnalog Devices AD743JR OpAmp. This transimpedance amplifier isparticularly advantageous in that it exhibits several desired featuresfor the system described, such as: low equivalent input voltage noise,low equivalent input current noise, low input bias current, high gainbandwidth product, low total harmonic distortion, high common moderejection, high open loop gain, and a high power supply rejection ratio.

[0241] The output of the preamplifier 342 couples as an input to thehigh pass filter 344. The output of the preamplifier also provides afirst input 346 to the analog to digital conversion circuit 332. In thepresent embodiment, the high pass filter is a single-pole filter with acorner frequency of about ½-1 Hz. However, the corner frequency isreadily raised to about 90 Hz in one embodiment. As will be understood,the 625 Hz carrier frequency of the red and infrared signals is wellabove a 90 Hz corner frequency. The high-pass filter 344 has an outputcoupled as an input to an amplifier 346. In the present embodiment, theamplifier 346 comprises a unity gain amplifier. However, the gain of theamplifier 346 is adjustable by the variation of a single resistor. Thegain of the amplifier 346 would be increased if the gain of thepreamplifier 342 is decreased to compensate for the effects of ambientlight.

[0242] The output of the amplifier 346 provides an input to aprogrammable gain amplifier 348. The programmable gain amplifier 348also accepts a programming input from the digital signal processingsystem 334 on a gain control signal line 343. The gain of theprogrammable gain amplifier 348 is digitally programmable. The gain isadjusted dynamically at initialization or sensor placement for changesin the medium under test from patient to patient. For example, thesignal from different fingers differs somewhat. Therefore, a dynamicallyadjustable amplifier is provided by the programmable gain amplifier 348in order to obtain a signal suitable for processing.

[0243] The programmable gain amplifier is also advantageous in analternative embodiment in which the emitter drive current is heldconstant. In the present embodiment, the emitter drive current isadjusted for each patient in order to obtain the proper dynamic range atthe input of the analog to digital conversion circuit 332. However,changing the emitter drive current can alter the emitter wavelength,which in turn affects the end result in oximetry calculations.Accordingly, it would be advantageous to fix the emitter drive currentfor all patients. In an alternative embodiment of the present invention,the programmable gain amplifier can be adjusted by the DSP in order toobtain a signal at the input to the analog to digital conversion circuitwhich is properly within the dynamic range (+3v to −3v in the presentembodiment) of the analog to digital conversion circuit 332. In thismanner, the emitter drive current could be fixed for all patients,eliminating the wavelength shift due to emitter current drive changes.

[0244] The output of the programmable gain amplifier 348 couples as aninput to a low-pass filter 350. Advantageously, the low pass filter 350is a single-pole filter with a corner frequency of approximately 10 Khzin the present embodiment. This low pass filter provides anti-aliasingin the present embodiment.

[0245] The output of the low-pass filter 350 provides a second input 352to the analog-to-digital conversion circuit 332. FIG. 12 also depictsadditional defect of the analog-to-digital conversion circuit. In thepresent embodiment, the analog-to-digital conversion circuit 332comprises a first analog-to-digital converter 354 and a secondanalog-to-digital converter 356. Advantageously, the firstanalog-to-digital converter 354 accepts input from the first input 346to the analog-to-digital conversion circuit 332, and the second analogto digital converter 356 accepts input on the second input 352 to theanalog-to-digital conversion circuitry 332.

[0246] In one advantageous embodiment, the first analog-to-digitalconverter 354 is a diagnostic analog-to-digital converter. Thediagnostic task (performed by the digital signal processing system) isto read the output of the detector as amplified by the preamplifier 342in order to determine if the signal is saturating the input to thehigh-pass filter 344. In the present embodiment, if the input to thehigh pass filter 344 becomes saturated, the front end analog signalconditioning circuits 330 provides a ‘0’ output. Alternatively, thefirst analog-to-digital converter 354 remains unused.

[0247] The second analog-to-digital converter 352 accepts theconditioned composite analog signal from the front end signalconditioning circuitry 330 and converts the signal to digital form. Inthe present embodiment, the second analog to digital converter 356comprises a single-channel, delta-sigma converter. In the presentembodiment, a Crystal Semiconductor CS5317-KS delta-sigma analog todigital converter is used. Such a converter is advantageous in that itis low cost, and exhibits low noise characteristics. More specifically,a delta-sigma converter consists of two major portions, a noisemodulator and a decimation filter. The selected converter uses a secondorder analog delta-sigma modulator to provide noise shaping. Noiseshaping refers to changing the noise spectrum from a flat response to aresponse where noise at the lower frequencies has been reduced byincreasing noise at higher frequencies. The decimation filter then cutsout the reshaped, higher frequency noise to provide 16-bit performanceat a lower frequency. The present converter samples the data 128 timesfor every 16 bit data word that it produces. In this manner, theconverter provides excellent noise rejection, dynamic range and lowharmonic distortion, that help in critical measurement situations likelow perfusion and electrocautery.

[0248] In addition, by using a single-channel converter, there is noneed to tune two or more channels to each other. The delta-sigmaconverter is also advantageous in that it exhibits noise shaping, forimproved noise control. An exemplary analog to digital converter is aCrystal Semiconductor CS5317. In the present embodiment, the secondanalog to digital converter 356 samples the signal at a 20 Khz samplerate. The output of the second analog to digital converter 356 providesdata samples at 20 Khz to the digital signal processing system 334 (FIG.11).

[0249] The digital signal processing system 334 is illustrated inadditional detail in FIG. 13. In the present embodiment, the digitalsignal processing system comprises a microcontroller 360, a digitalsignal processor 362, a program memory 364, a sample buffer 366, a datamemory 368, a read only memory 370 and communication registers 372. Inthe present embodiment, the digital signal processor 362 is an AnalogDevices AD 21020. In the present embodiment, the microcontroller 360comprises a Motorola 68HC05, with built in program memory. In thepresent embodiment, the sample buffer 366 is a buffer which accepts the20 Khz sample data from the analog to digital conversion circuit 332 forstorage in the data memory 368. In the present embodiment, the datamemory 368 comprises 32 KWords (words being 40 bits in the presentembodiment) of static random access memory.

[0250] The microcontroller 360 is connected to the DSP 362 via aconventional JTAG Tap line. The microcontroller 360 transmits the bootloader for the DSP 362 to the program memory 364 via the Tap line, andthen allows the DSP 362 to boot from the program memory 364. The bootloader in program memory 364 then causes the transfer of the operatinginstructions for the DSP 362 from the read only memory 370 to theprogram memory 364. Advantageously, the program memory 364 is a veryhigh speed memory for the DSP 362.

[0251] The microcontroller 360 provides the emitter current control andgain control signals via the communications register 372.

[0252]FIGS. 14-20 depict functional block diagrams of the operations ofthe pulse oximeter 299 carried out by the digital signal processingsystem 334. The signal processing functions described below are carriedout by the DSP 362 in the present embodiment with the microcontroller360 providing system management. In the present embodiment, theoperation is software/firmware controlled. FIG. 14 depicts a generalizedfunctional block diagram for the operations performed on the 20 Khzsample data entering the digital signal processing system 334. Asillustrated in FIG. 14, a demodulation, as represented in a demodulationmodule 400, is first performed. Decimation, as represented in adecimation module 402 is then performed on the resulting data. Certainstatistics are calculated, as represented in a statistics module 404 anda saturation transform is performed, as represented in a saturationtransform module 406, on the data resulting from the decimationoperation. The data subjected to the statistics operations and the datasubjected to the saturation transform operations are forwarded tosaturation operations, as represented by a saturation calculation module408 and pulse rate operations, as represented in a pulse ratecalculation module 410.

[0253] In general, the demodulation operation separates the red andinfrared signals from the composite signal and removes the 625 Hzcarrier frequency, leaving raw data points. The raw data points areprovided at 625 Hz intervals to the decimation operation which reducesthe samples by an order of 10 to samples at 62.5 Hz. The decimationoperation also provides some filtering on the samples. The resultingdata is subjected to statistics and to the saturation transformoperations in order to calculate a saturation value which is verytolerant to motion artifacts and other noise in the signal. Thesaturation value is ascertained in the saturation calculation module408, and a pulse rate and a clean plethysmographic waveform is obtainedthrough the pulse rate module 410. Additional detail regarding thevarious operations is provided in connection with FIGS. 15-21.

[0254]FIG. 15 illustrates the operation of the demodulation module 400.The modulated signal format is depicted in FIG. 15. One full 625 Hzcycle of the composite signal is depicted in FIG. 15 with the firstquarter cycle being the active red light plus ambient light signal, thesecond quarter cycle being an ambient light signal, the third quartercycle being the active infrared plus ambient light signal, and thefourth quarter cycle being an ambient light signal. As depicted in FIG.15, with a 20 KHz sampling frequency, the single full cycle at 625 Hzdescribed above comprises 32 samples of 20 KHz data, eight samplesrelating to red plus ambient light, eight samples relating to ambientlight, eight samples relating to infrared plus ambient light, andfinally eight samples related to ambient light.

[0255] Because the signal processing system 334 controls the activationof the light emitters 300, 302, the entire system is synchronous. Thedata is synchronously divided (and thereby demodulated) into four8-sample packets, with a time division demultiplexing operation asrepresented in a demultiplexing module 421. One eight-sample packet 422represents the red plus ambient light signal; a second eight-samplepacket 424 represents an ambient light signal; a third eight-samplepacket 426 represents the attenuated infrared light plus ambient lightsignal; and a fourth eight-sample packet 428 represents the ambientlight signal. A select signal synchronously controls the demultiplexingoperation so as to divide the time-division multiplexed composite signalat the input of the demultiplexer 421 into its four subparts.

[0256] A sum of the last four samples from each packet is thencalculated, as represented in the summing operations 430, 432, 434, 436of FIG. 15. In the present embodiment, the last four samples are usedbecause a low pass filter in the analog to digital converter 356 of thepresent embodiment has a settling time. Thus, collecting the last foursamples from each 8-sample packet allows the previous signal to clear.This summing operation provides an integration operation which enhancesnoise immunity. The sum of the respective ambient light samples is thensubtracted from the sum of the red and infrared samples, as representedin the subtraction modules 438, 440. The subtraction operation providessome attenuation of the ambient light signal present in the data. In thepresent embodiment, it has been found that approximately 20 dBattenuation of the ambient light is provided by the operations of thesubtraction modules 438, 440. The resultant red and infrared sum valuesare divided by four, as represented in the divide by four modules 442,444. Each resultant value provides one sample each of the red andinfrared signals at 625 Hz.

[0257] It should be understood that the 625 Hz carrier frequency hasbeen removed by the demodulation operation 400. The 625 Hz sample dataat the output of the demodulation operation 400 is sample data withoutthe carrier frequency. In order to satisfy Nyquist samplingrequirements, less than 20 Hz is needed (understanding that the humanpulse is about 25 to 250 beats per minute, or about 0.4 Hz-4 Hz).Accordingly, the 625 Hz resolution is reduced to 62.5 Hz in thedecimation operation.

[0258]FIG. 16 illustrates the operations of the decimation module 402.The red and infrared sample data is provided at 625 Hz to respective redand infrared buffer/filters 450, 452. In the present embodiment, the redand infrared buffer/filters are 519 samples deep. Advantageously, thebuffer filters 450, 452 function as continuous first-in, first-outbuffers. The 519 samples are subjected to low-pass filtering.Preferably, the low-pass filtering has a cutoff frequency ofapproximately 7.5 Hz with attenuation of approximately—110 dB. Thebuffer/filters 450, 452 form a Finite Impulse Response (FIR) filter withcoefficients for 519 taps. In order to reduce the sample frequency byten, the low-pass filter calculation is performed every ten samples, asrepresented in respective red and infrared decimation by 10 modules 454,456. In other words, with the transfer of each new ten samples into thebuffer/filters 450, 452, a new low pass filter calculation is performedby multiplying the impulse response (coefficients) by the 519 filtertaps. Each filter calculation provides one output sample for respectivered and infrared output buffers 458, 460. In the present embodiment, thered and infrared output buffers 458, 460 are also continuous FIFObuffers that hold 570 samples of data. The 570 samples providerespective infrared and red samples or packets (also denoted “snapshot”herein) of samples. As depicted in FIG. 14, the output buffers providesample data for the statistics operation module 404, saturationtransform module 406, and the pulse rate module 410.

[0259]FIG. 17 illustrates additional functional operation details of thestatistics module 404. In summary, the statistics module 404 providesfirst order oximetry calculations and RMS signal values for the red andinfrared channels. The statistics module also provides across-correlation output which indicates a cross-correlation between thered and infrared signals.

[0260] As represented in FIG. 17, the statistics operation accepts twopackets of samples (e.g., 570 samples at 62.5 Hz in the presentembodiment) representing the attenuated infrared and red signals, withthe carrier frequency removed. The respective packets for infrared andred signals are normalized with a log function, as represented in theLog modules 480, 482. The normalization is followed by removal of the DCportion of the signals, as represented in the DC Removal modules 484,486. In the present embodiment, the DC removal involves ascertaining theDC value of the first one of the samples (or the mean of the firstseveral or the mean of an entire snapshot) from each of the respectivered and infrared snapshots, and removing this DC value from all samplesin the respective packets.

[0261] Once the DC signal is removed, the signals are subjected tobandpass filtering, as represented in red and infrared Bandpass Filtermodules 488, 490. In the present embodiment, with 570 samples in eachpacket, the bandpass filters are configured with 301 taps to provide aFIR filter with a linear phase response and little or no distortion. Inthe present embodiment, the bandpass filter has a pass band from 34beats/minute to 250 beats/minute. The 301 taps slide over the 570samples in order to obtain 270 filtered samples representing thefiltered red signal and 270 filtered samples representing the filteredinfrared signal. In an ideal case, the bandpass filters 488, 490 removethe DC in the signal. However, the DC removal operations 484, 486 assistin DC removal in the present embodiment.

[0262] After filtering, the last 120 samples from each packet (of now270 samples in the present embodiment) are selected for furtherprocessing as represented in Select Last 120 Samples modules 492, 494.The last 120 samples are selected because, in the present embodiment,the first 150 samples fall within the settling time for the SaturationTransfer module 406, which processes the same data packets, as furtherdiscussed below.

[0263] Conventional saturation equation calculations are performed onthe red and infrared 120-sample packets. In the present embodiment, theconventional saturation calculations are performed in two differentways. For one calculation, the 120-sample packets are processed toobtain their overall RMS value, as represented in the first red andinfrared RMS modules 496, 498. The resultant RMS values for red andinfrared signals provide input values to a first RED_RMS/IR_RMS ratiooperation 500, which provides the RMS red value to RMS infrared valueratio as an input to a saturation equation module 502. As wellunderstood in the art, the ratio of the intensity of red to infraredattenuated light as detected for known red and infrared wavelengths(typically λ_(red)=650 nm and λ_(IR)=910 nm) relates to the oxygensaturation of the patient. Accordingly, the saturation equation module502 represents a conventional look-up table or the like which, forpredetermined ratios, provides known saturation values at its output504. The red and infrared RMS values are also provided as outputs of thestatistics operations module 404.

[0264] In addition to the conventional saturation operation 502, the120-sample packets are subjected to a cross-correlation operation asrepresented in a first cross-correlation module 506. The firstcross-correlation module 506 determines if good correlation existsbetween the infrared and red signals. This cross correlation isadvantageous for detecting defective or otherwise malfunctioningdetectors. The cross correlation is also advantageous in detecting whenthe signal model (i.e., the model of Equations (1)-(3)) is satisfied. Ifcorrelation becomes too low between the two channels, the signal modelis not met. In order to determine this, the normalized cross correlationcan be computed by the cross-correlation module 506 for each snapshot ofdata. One such correlation function is as follows:$\frac{\sum{s_{1}s_{2}}}{\sqrt{\sum{s_{1}^{2}s_{2}^{2}}}}$

[0265] If the cross correlation is too low, the oximeter 299 provides awarning (e.g., audible, visual, etc.) to the operator. In the presentembodiment, if a selected snapshot yields a normalized correlation ofless than 0.75, the snapshot does not qualify. Signals which satisfy thesignal model will have a correlation greater than the threshold.

[0266] The red and infrared 120-sample packets are also subjected to asecond saturation operation and cross correlation in the same manner asdescribed above, except the 120 samples are divided into 5 equal bins ofsamples (i.e., 5 bins of 24 samples each). The RMS, ratio, saturation,and cross correlation operations are performed on a bin-by-bin basis.These operations are represented in the Divide Into Five Equal Binsmodules 510, 512, the second red and infrared RMS modules 514, 516, thesecond RED-RMS/IR-RMS ratio module 518, the second saturation equationmodule 520 and the second cross correlation module 522 in FIG. 17.

[0267]FIG. 18 illustrates additional detail regarding the saturationtransform module 406 depicted in FIG. 14. As illustrated in FIG. 18, thesaturation transform module 406 comprises a reference processor 530, acorrelation canceler 531, a master power curve module 554, and a binpower curve module 533. The saturation transform module 406 can becorrelated to FIG. 7a which has a reference processor 26 and acorrelation canceler 27 and an integrator 29 to provide a power curvefor separate signal coefficients as depicted in FIG. 7c. The saturationtransform module 406 obtains a saturation spectrum from the snapshots ofdata. In other words, the saturation transform 406 provides informationof the saturation values present in the snapshots.

[0268] As depicted in FIG. 18, the reference processor 530 for thesaturation transform module 406 has a saturation equation module 532, areference generator module 534, a DC removal module 536 and a bandpassfilter module 538. The red and infrared 570—sample packets from thedecimation operation are provided to the reference processor 530. Inaddition, a plurality of possible saturation values (the “saturationaxis scan”) are provided as input to the saturation reference processor530. In the present embodiment, 117 saturation values are provided asthe saturation axis scan. In a preferred embodiment, the 117 saturationvalues range uniformly from a blood oxygen saturation of 34.8 to 105.0.Accordingly, in the present embodiment, the 117 saturation valuesprovide an axis scan for the reference processor 530 which generates areference signal for use by the correlation canceler 531. In otherwords, the reference processor is provided with each of the saturationvalues, and a resultant reference signal is generated corresponding tothe saturation value. The correlation canceler is formed by a jointprocess estimator 550 and a low pass filter 552 in the presentembodiment.

[0269] It should be understood that the scan values could be chosen toprovide higher or lower resolution than 117 scan values. The scan valuescould also be non-uniformly spaced.

[0270] As illustrated in FIG. 18, the saturation equation module 532accepts the saturation axis scan values as an input and provides a ratio“r_(n)” as an output. In comparison to the general discussion of FIG.7a-7 c, this ratio “r_(n)” corresponds to the plurality of scan valuediscussed above in general. The saturation equation simply provides aknown ratio “r” (red/infrared) corresponding to the saturation valuereceived as an input.

[0271] The ratio “r_(n)” is provided as an input to the referencegenerator 534, as are the red and infrared sample packets. The referencegenerator 534 multiplies either the red or infrared samples by the ratio“r_(n)” and subtracts the value from the infrared or red samples,respectively. For instance, in the present embodiment, the referencegenerator 534 multiplies the red samples by the ratio “r_(n)” andsubtracts this value from the infrared samples. The resulting valuesbecome the output of the reference generator 534. This operation iscompleted for each of the saturation scan values (e.g., 117 possiblevalues in the present embodiment). Accordingly, the resultant data canbe described as 117 reference signal vectors of 570 data points each,hereinafter referred to as the reference signal vectors. This data canbe stored in an array or the like.

[0272] In other words, assuming that the red and infrared sample packetsrepresent the red S_(red)(t) and infrared S_(IR)(t) measured signalswhich have primary s(t) and secondary n(t) signal portions, the outputof the reference generator becomes the secondary reference signal n′(t),which complies with the signal model defined above, as follows:

n′(t)=s _(ir)(t)−r _(n) s _(red)(t)

[0273] In the present embodiment, the reference signal vectors and theinfrared signal are provided as input to the DC removal module 536 ofthe reference processor 530. The DC removal module 536, like the DCremoval modules 484, 486 in the statistics module 404, ascertains the DCvalue of the first of the samples for the respective inputs (or mean ofthe first several or all samples in a packet) and subtracts therespective DC baseline from the sample values. The resulting samplevalues are subjected to a bandpass filter 538.

[0274] The bandpass filter 538 of the reference processor 530 performsthe same type of filtering as the bandpass filters 488, 490 of thestatistics module 404. Accordingly, each set of 570 samples subjected tobandpass filtering results in 270 remaining samples. The resulting dataat a first output 542 of the bandpass filter 538 is one vector of 270samples (representing the filtered infrared signal in the presentembodiment). The resulting data at a second output 540 of the bandpassfilter 538, therefore, is 117 reference signal vectors of 270 datapoints each, corresponding to each of the saturation axis scan valuesprovided to the saturation reference processor 530.

[0275] It should be understood that the red and infrared sample packetsmay be switched in their use in the reference processor 530. Inaddition, it should be understood that the DC removal module 536 and thebandpass filter module 538 can be executed prior to input of the data tothe reference processor 530 because the calculations performed in thereference processor are linear. This results in a significant processingeconomy.

[0276] The outputs of the reference processor 530 provide first andsecond inputs to a joint process estimator 550 of the type describedabove with reference to FIG. 8. The first input to the joint processestimator 550 is the 270-sample packet representing the infrared signalin the present embodiment. This signal contains primary and secondarysignal portions. The second input to the joint process estimator is the117 reference signal vectors of 270 samples each.

[0277] The joint process estimator also receives a lambda input 543, aminimum error input 544 and a number of cells configuration input 545.These parameters are well understood in the art. The lambda parameter isoften called the “forgetting parameter” for a joint process estimator.The lambda input 543 provides control for the rate of cancellation forthe joint process estimator. In the present embodiment, lambda is set toa low value such as 0.8. Because statistics of the signal arenon-stationary, a low value improves tracking. The minimum error input544 provides an initialization parameter (conventionally known as the“initialization value”) for the joint process estimator 550. In thepresent embodiment, the minimum error value is 10⁻⁶. This initializationparameter prevents the joint process estimator 500 from dividing by zeroupon initial calculations. The number of cells input 545 to the jointprocess estimator 550 configures the number of cells for the jointprocess estimator. In the present embodiment, the number of cells forthe saturation transform operation 406 is six. As well understood in theart, for each sine wave, the joint process estimator requires two cells.If there are two sine waves in the 35-250 beats/minute range, six cellsallows for the two heart beat sine waves and one noise sine wave.

[0278] The joint process estimator 550 subjects the first input vectoron the first input 542 to a correlation cancellation based upon each ofthe plurality of reference signal vectors provided in the second input540 to the correlation canceler 531 (all 117 reference vectors insequence in the present embodiment). The correlation cancellationresults in a single output vector for each of the 117 reference vectors.Each output vector represents the information that the first inputvector and the corresponding reference signal vector do not have incommon. The resulting output vectors are provided as an output to thejoint process estimator, and subjected to the low pass filter module552. In the present embodiment, the low pass filter 552 comprises a FIRfilter with 25 taps and with a corner frequency of 10 Hz with thesampling frequency of 62.5 Hz (i.e., at the decimation frequency).

[0279] The joint process estimator 550 of the present embodiment has asettling time of 150 data points. Therefore, the last 120 data pointsfrom each 270 point output vector are used for further processing. Inthe present embodiment, the output vectors are further processedtogether as a whole, and are divided into a plurality of bins of equalnumber of data points. As depicted in FIG. 18, the output vectors areprovided to a master power curve module 554 and to a Divide into fiveEqual Bins module 556. The Divide into Five Equal Bins module 556divides each of the output vectors into five bins of equal number ofdata points (e.g. with 120 data points per vector, each bin has 24 datapoints). Each bin is then provided to the Bin Power Curves module 558.

[0280] The Master Power Curve module 554 performs a saturation transformas follows: for each output vector, the sum of the squares of the datapoints is ascertained. This provides a sum of squares valuecorresponding to each output vector (each output vector corresponding toone of the saturation scan values). These values provide the basis for amaster power curve 555, as further represented in FIG. 22. Thehorizontal axis of the power curve represents the saturation axis scanvalues and the vertical axis represents the sum of squares value (oroutput energy) for each output vector. In other words, as depicted inFIG. 22, each of the sum of squares could be plotted with the magnitudeof the sum of squares value plotted on the vertical “energy output” axisat the point on the horizontal axis of the corresponding saturation scanvalue which generated that output vector. This results in a master powercurve 558, an example of which is depicted in FIG. 22. This provides asaturation transform in which the spectral content of the attenuatedenergy is examined by looking at every possible saturation value andexamining the output value for the assumed saturation value. As will beunderstood, where the first and second inputs to the correlationcanceler 531 are mostly correlated, the sum of squares for thecorresponding output vector of the correlation canceler 531 will be verylow. Conversely, where the correlation between the first and secondinputs to the correlation canceler 531 are not significantly correlated,the sum of squares of the output vector will be high. Accordingly, wherethe spectral content of the reference signal and the first input to thecorrelation canceler are made up mostly of physiological (e.g., movementof venous blood due to respiration) and non-physiological (e.g., motioninduced) noise, the output energy will be low. Where the spectralcontent of the reference signal and the first input to the correlationcanceler are not correlated, the output energy will be much higher.

[0281] A corresponding transform is completed by the Bin Power Curvesmodule 558, except a saturation transform power curve is generated foreach bin. The resulting power curves are provided as the outputs of thesaturation transform module 406.

[0282] In general, in accordance with the signal model of the presentinvention, there will be two peaks in the power curves, as depicted inFIG. 22. One peak corresponds to the arterial oxygen saturation of theblood, and one peak corresponds to the venous oxygen concentration ofthe blood. With reference to the signal model of the present invention,the peak corresponding to the highest saturation value (not necessarilythe peak with the greatest magnitude) corresponds to the proportionalitycoefficient r_(a). In other words, the proportionality coefficient r_(a)corresponds to the red/infrared ratio which will be measured for thearterial saturation. Similarly, peak that corresponds to the lowestsaturation value (not necessarily the peak with the lowest magnitude)will generally correspond to the venous oxygen saturation, whichcorresponds to the proportionality coefficient r_(v) in the signal modelof the present invention. Therefore, the proportionality coefficient r,will be a red/infrared ratio corresponding to the venous oxygensaturation.

[0283] In order to obtain arterial oxygen saturation, the peak in thepower curves corresponding to the highest saturation value could beselected. However, to improve confidence in the value, furtherprocessing is completed. FIG. 19 illustrates the operation of thesaturation calculation module 408 based upon the output of thesaturation transform module 406 and the output of the statistics module404. As depicted in FIG. 19, the bin power curves and the bin statisticsare provided to the saturation calculation module 408. In the presentembodiment, the master power curves are not provided to the saturationmodule 408 but can be displayed for a visual check on system operation.The bin statistics contain the red and infrared RMS values, the seedsaturation value, and a value representing the cross-correlation betweenthe red and infrared signals from the statistics module 404.

[0284] The saturation calculation module 408 first determines aplurality of bin attributes as represented by the Compute Bin Attributesmodule 560. The Compute Bin Attributes module 560 collects a data binfrom the information from the bin power curves and the information fromthe bin statistics. In the present embodiment, this operation involvesplacing the saturation value of the peak from each power curvecorresponding to the highest saturation value in the data bin. In thepresent embodiment, the selection of the highest peak is performed byfirst computing the first derivative of the power curve in question byconvolving the power curve with a smoothing differentiator filterfunction. In the present embodiment, the smoothing differentiator filterfunction (using a FIR filter) has the following coefficients:

[0285] 0.014964670230367

[0286] 0.098294046682706

[0287] 0.204468276324813

[0288] 2.717182664241813

[0289] 5.704485606695227

[0290] 0.000000000000000

[0291] −5.704482606695227

[0292] −2.717182664241813

[0293] −0.204468276324813

[0294] −0.098294046682706

[0295] −0.014964670230367

[0296] This filter performs the differentiation and smoothing. Next,each point in the original power curve in question is evaluated anddetermined to be a possible peak if the following conditions are met:(1) the point is at least 2% of the maximum value in the power curve;(2) the value of the first derivative changes from greater than zero toless than or equal to zero. For each point that is found to be apossible peak, the neighboring points are examined and the largest ofthe three points is considered to be the true peak.

[0297] The peak width for these selected peaks is also calculated. Thepeak width of a power curve in question is computed by summing all thepoints in the power curve and subtracting the product of the minimumvalue in the power curve and the number of points in the power curve. Inthe present embodiment, the peak width calculation is applied to each ofthe bin power curves. The maximum value is selected as the peak width.

[0298] In addition, the infrared RMS value from the entire snapshot, thered RMS value, the seed saturation value for each bin, and the crosscorrelation between the red and infrared signals from the statisticsmodule 404 are also placed in the data bin. The attributes are then usedto determine whether the data bin consists of acceptable data, asrepresented in a Bin Qualifying Logic module 562.

[0299] If the correlation between the red and infrared signals is toolow, the bin is discarded. If the saturation value of the selected peakfor a given bin is lower than the seed saturation for the same bin, thepeak is replaced with the seed saturation value. If either red orinfrared RMS value is below a very small threshold, the bins are alldiscarded, and no saturation value is provided, because the measuredsignals are considered to be too small to obtain meaningful data. If nobins contain acceptable data, the exception handling module 563 providesa message to the display 336 that the data is erroneous.

[0300] If some bins qualify, those bins that qualify as havingacceptable data are selected, and those that do not qualify are replacedwith the average of the bins that are accepted. Each bin is given a timestamp in order to maintain the time sequence. A voter operation 565examines each of the bins and selects the three highest saturationvalues. These values are forwarded to a clip and smooth operation 566.

[0301] The clip and smooth operation 566 basically performs averagingwith a low pass filter. The low pass filter provides adjustablesmoothing as selected by a Select Smoothing Filter module 568. TheSelect Smoothing Filter module 568 performs its operation based upon aconfidence determination performed by a High Confidence Test module 570.The high confidence test is an examination of the peak width for the binpower curves. The width of the peaks provides some indication of motionby the patient—wider peaks indicating motion. Therefore, if the peaksare wide, the smoothing filter is slowed down. If peaks are narrow, thesmoothing filter speed is increased. Accordingly, the smoothing filter566 is adjusted based on the confidence level. The output of the clipand smooth module 566 provides the oxygen saturation values inaccordance with the present invention.

[0302] In the presently preferred embodiment, the clip and smooth filter566 takes each new saturation value and compares it to the currentsaturation value. If the magnitude of the difference is less than 16(percent oxygen saturation) then the value is pass. Otherwise, if thenew saturation value is less than the filtered saturation value, the newsaturation value is changed to 16 less than the filtered saturationvalue. If the new saturation value is greater than the filteredsaturation value, then the new saturation value is changed to 16 morethan the filtered saturation value.

[0303] During high confidence (no motion), the smoothing filter is asimple one-pole or exponential smoothing filter which is computed asfollows:

y(n)=0.6*x(n)+0.4*y(n−1)

[0304] where x(n) is the clipped new saturation value, and y(n) is thefiltered saturation value.

[0305] During motion condition, a three-pole IIR (infinite impulseresponse) filter is used. Its characteristics are controlled by threetime constants t_(a), t_(b), and t_(c) with values of 0.985, 0.900, and0.94 respectively. The coefficients for a direct form I, IIR filter arecomputed from these time constants using the following relationships:

a₀=0

a ₁ =t _(b)+(t _(c))(t _(a) +t _(b))

^(a) ₂=(−t _(b))(t _(c))(t _(a) +t _(b)+(tc)(t _(a)))

a ₃=(t _(b))²(t _(c))²(t _(a))

b ₀=1−t _(b)−(t _(c))(t _(a)+(t _(c))(t _(b)))

b ₁=2(t _(b))(t _(c))(t _(a)−1)

b ₂=(t _(b))(t _(c))(t _(b)+(t _(c))(t _(a))−(t _(b))(t _(c))(t _(a))−t_(a))

[0306]FIGS. 20 and 21 illustrate the pulse rate module 410 (FIG. 14) ingreater detail. As illustrated in FIG. 20, the heart rate module 410 hasa transient removal and bandpass filter module 578, a motion artifactsuppression module 580, a saturation equation module 582, a motionstatus module 584, first and second spectral estimation modules 586,588, a spectrum analysis module 590, a slew rate limiting module 592, anoutput filter 594, and an output filter coefficient module 596.

[0307] As further depicted in FIG. 20, the heart rate module 410 acceptsthe infrared and red 570-sample snapshots from the output of thedecimation module 402. The heart rate module 410 further accepts thesaturation value which is output from the saturation calculation module408. In addition, the maximum peak width as calculated by the confidencetest module 570 (same as peak width calculation described above) is alsoprovided as an input to the heart rate module 410. The infrared and redsample packets, the saturation value and the output of the motion statusmodule 584 are provided to the motion artifact suppression module 580.

[0308] The average peak width value provides an input to a motion statusmodule 584. In the present embodiment, if the peaks are wide, this istaken as an indication of motion. If motion is not detected, spectralestimation on the signals is carried out directly without motionartifact suppression.

[0309] In the case of motion, motion artifacts are suppressed using themotion artifact suppression module 580. The motion artifact suppressionmodule 580 is nearly identical to the saturation transform module 406.The motion artifact suppression module 580 provides an output whichconnects as an input to the second spectral estimation module 588. Thefirst and second spectral estimation modules 586, 588 have outputs whichprovide inputs to the spectrum analysis module 590. The spectrumanalysis module 590 also receives an input which is the output of themotion status module 584. The output of the spectrum analysis module 590is the initial heart rate determination of the heart rate module 410 andis provided as input to the slew rate limiting module 592. The slew ratelimiting module 592 connects to the output filter 594. The output filter594 also receives an input from the output filter coefficient module596. The output filter 594 provides the filtered heart rate for thedisplay 336 (FIG. 11).

[0310] In the case of no motion, one of the signals (the infrared signalin the present embodiment) is subjected to DC removal and bandpassfiltering as represented in the DC removal and bandpass filter module578. The DC removal and bandpass filter module 578 provide the samefiltering as the DC removal and bandpass filter modules 536, 538. Duringno motion conditions, the filtered infrared signal is provided to thefirst spectral estimation module 586.

[0311] In the present embodiment, the spectral estimation comprises aChirp Z transform that provides a frequency spectrum of heart rateinformation. The Chirp Z transform is used rather than a conventionalFourier Transform because a frequency range for the desired output canbe designated in a Chirp Z transform. Accordingly, in the presentembodiment, a frequency spectrum of the heart rate is provided between30 and 250 beats/minute. In the present embodiment, the frequencyspectrum is provided to a spectrum analysis module 590 which selects thefirst harmonic from the spectrum as the pulse rate. Usually, the firstharmonic is the peak in the frequency spectrum that has the greatestmagnitude and represents the pulse rate. However, in certain conditions,the second or third harmonic can exhibit the greater magnitude. Withthis understanding, in order to select the first harmonic, the firstpeak that has an amplitude of at least {fraction (1/20)}th of thelargest peak in the spectrum is selected). This minimizes thepossibility of selecting as the heart rate a peak in the Chirp Ztransform caused by noise.

[0312] In the case of motion, a motion artifact suppression is completedon the snapshot with the motion artifact suppression module 580. Themotion artifact suppression module 580 is depicted in greater detail inFIG. 21. As can be seen in FIG. 21, the motion artifact suppressionmodule 580 is nearly identical to the saturation transform module 406(FIG. 18). Accordingly, the motion artifact suppression module has amotion artifact reference processor 570 and a motion artifactcorrelation canceler 571.

[0313] The motion artifact reference processor 570 is the same as thereference processor 530 of the saturation transform module 406. However,the reference processor 570 utilizes the saturation value from thesaturation module 408, rather than completing an entire saturationtransform with the 117 saturation scan values. The reference processor570, therefore, has a saturation equation module 581, a referencegenerator 582, a DC removal module 583, and a bandpass filter module585. These modules are the same as corresponding modules in thesaturation transform reference processor 530. In the present embodiment,the saturation equation module 581 receives the arterial saturationvalue from the saturation calculation module 408 rather than doing asaturation axis scan as in the saturation transform module 406. This isbecause the arterial saturation has been selected, and there is no needto perform an axis scan. Accordingly, the output of the saturationequation module 581 corresponds to the proportionality constant ra(i.e., the expected red to infrared ratio for the arterial saturationvalue). Otherwise, the reference processor 570 performs the samefunction as the reference processor 530 of the saturation transformmodule 406.

[0314] The motion artifact correlation canceler 571 is also similar tothe saturation transform correlation canceler 531 (FIG. 18). However,the motion artifact suppression correlation canceler 571 uses a slightlydifferent motion artifact joint process estimator 572. Accordingly, themotion artifact suppression correlation canceler 571 has a joint processestimator 572 and a low-pass filter 573. The motion artifact jointprocess estimator 572 differs from the saturation transform jointprocess estimator 550 in that there are a different number of cells(between 6 and 10 in the present embodiment), as selected by the Numberof Cells input 574, in that the forgetting parameter differs (0.98 inthe present embodiment), and in that the time delay due to adaptationdiffers. The low-pass filter 573 is the same as the low pass filter 552of the saturation transform correlation canceler 531.

[0315] Because only one saturation value is provided to the referenceprocessor, only one output vector of 270 samples results at the outputof the motion artifact suppression correlation canceler 571 for eachinput packet of 570 samples. In the present embodiment, where theinfrared wavelength is provided as a first input toe the correlationcanceler, the output of the correlation canceler 571 provides a cleaninfrared waveform. It should be understood that, as described above, theinfrared and red wavelength signals could be switched such that a cleanred waveform is provided at the output of the motion artifactsuppression correlation canceler 571. The output of the correlationcanceler 571 is a clean waveform because the actual saturation value ofthe patient is known which allows the reference processor 570 togenerate a noise reference for inputting to the correlation canceler 571as the reference signal. The clean waveform at the output of the motionartifact suppression module 580 is a clean plethysmograph waveform whichcan be forwarded to the display 336.

[0316] As described above, an alternative joint process estimator usesthe QRD least squares lattice approach (FIGS. 8a, 9 a and 10 a).Accordingly, the joint process estimator 573 (as well as the jointprocess estimator 550) could be replaced with a joint process estimatorexecuting the QRD least squares lattice operation.

[0317]FIG. 21a depicts an alternative embodiment of the motion artifactsuppression module with a joint process estimator 572 a replacing thejoint process estimator 572. The joint process estimator 572 a comprisesa QRD least squares lattice system as in FIG. 10a. In accordance withthis embodiment, different initialization parameters are used asnecessary for the QRD algorithm.

[0318] The initialization parameters are referenced in FIG. 21a as“Number of Cells,” “Lambda,” “MinSumErr,” “GamsInit,” and “SumErrInit.”Number of Cells and Lambda correspond to like parameters in the jointprocess estimator 572. GamsInit corresponds to the y initializationvariable for all stages except the zero order stage, which as set forthin the QRD equations above is initialized to ‘1’. SummErrInit providesthe 6 initialization parameter referenced above in the QRD equations. Inorder to avoid overflow, the larger of the actual calculated denominatorin each division in the QRD equations and MinSumErr is used. In thepresent embodiment, the preferred initialization parameters are asfollows:

[0319] Number of Cells=6

[0320] Lambda=0.8

[0321] MinSumErr=11002

[0322] GamsInit=10⁻²

[0323] SumErrInit=10⁻⁶.

[0324] The clean waveform output from the motion artifact suppressionmodule 580 also provides an input to the second spectral estimationmodule 588. The second spectral estimation module 588 performs the sameChirp Z transform as the first spectral estimation module 586. In thecase of no motion, the output from the first spectral estimation module586 is provided to the spectrum analysis module 586; in the case ofmotion, the output from the second spectral estimation module 588 isprovided to a spectrum analysis module 590. The spectrum analysis module590 examines the frequency spectrum from the appropriate spectralestimation module to determine the pulse rate. In the case of motion,the spectrum analysis module 590 selects the peak in the spectrum withthe highest amplitude, because the motion artifact suppression module580 attenuates all other frequencies to a value below the actual heartrate peak. In the case of no motion, the spectrum analysis moduleselects the first harmonic in the spectrum as the heart rate asdescribed above.

[0325] The output of the spectrum analysis module 590 provides the rawheart rate as an input to the slew rate limiting module 592, whichprovides an input to an output filter 594. In the present embodiment,the slew rate limiting module 592 prevents changes greater that 20beats/minute per 2 second interval.

[0326] The output filter 594 comprises an exponential smoothing filtersimilar to the exponential smoothing filter described above with respectto the clip and smooth filter 566. The output filter is controlled viaan output filter coefficient module 596. If motion is large, this filteris slowed down, if there is little or no motion, this filter can samplemuch faster and still maintain a clean value. The output from the outputfilter 594 is the pulse of the patient, which is advantageously providedto the display 336.

[0327] Alternative To Saturation Transform Module—Bank Of Filters

[0328] An alternative to the saturation transform of the saturationtransform module 406 can be implemented with a bank of filters asdepicted in FIG. 23. As seen in FIG. 23, two banks of filters, a firstfilter bank 600 and a second filter bank 602 are provided. The firstfilter bank 600 receives a first measured signal S_(λb)(t) (the infraredsignal samples in the present embodiment) on a corresponding firstfilter bank input 604, and the second filter bank 602 receives a secondmeasured signal S_(λa)(t) (the red samples in the present embodiment) ona corresponding second filter bank input 606. In a preferred embodiment,the first and second filter banks utilize static recursive polyphasebandpass filters with fixed center frequencies and corner frequencies.Recursive polyphase filters are described in an article Harris, et. al.“Digital Signal Processing With Efficient Polyphase Recursive All-Passfilters” attached hereto as Appendix A. However, adaptiveimplementations are also possible. In the present implementation, therecursive polyphase bandpass filter elements are each designed toinclude a specific center frequency and bandwidth.

[0329] There are N filter elements in each filter bank. Each of thefilter elements in the first filter bank 600 have a matching (i.e., samecenter frequency and bandwidth) filter element in the second filter bank602. The center frequencies and the corner frequencies of N elements areeach designed to occupy N frequency ranges, 0 to F₁, F₁-F₂, F₂-F₃, F₃-F₄. . . F_(N−1)-F_(N) as shown in FIG. 23.

[0330] It should be understood that the number of filter elements canrange from 1 to infinity. However, in the present embodiment, there areapproximately 120 separate filter elements with center frequenciesspread evenly across a frequency range of 25 beats/minute-250beats/minute.

[0331] The outputs of the filters contain information about the primaryand secondary signals for the first and second measured signals (red andinfrared in the present example) at the specified frequencies. Theoutputs for each pair of matching filters (one in the first filter bank600 and one in the second filter bank 602) are provided to saturationdetermination modules 610. FIG. 23 depicts only one saturationdetermination module 610 for ease of illustration. However, a saturationdetermination module can be provided for each matched pair of filterelements for parallel processing. Each saturation determination modulehas a ratio module 616 and a saturation equation module 618.

[0332] The ratio module 616 forms a ratio of the second output to thefirst output. For instance, in the present example, a ratio of each redRMS value to each corresponding infrared RMS value (Red/IR) is completedin the ratio module 616. The output of the ratio module 616 provides aninput to the saturation equation module 618 which references acorresponding saturation value for the input ratio.

[0333] The output of the saturation equation modules 618 are collected(as represented in the histogram module 620) for each of the matchedfilter pairs. However, the data collected is initially a function offrequency and saturation. In order to form a saturation transform curvesimilar to the curve depicted in FIG. 22, a histogram or the like isgenerated as in FIG. 24. The horizontal axis represents the saturationvalue, and the vertical axis represents a summation of the number ofpoints (outputs from the saturation equation modules 618) collected ateach saturation value. In other words, if the output of the saturationequation module 618 for ten different matched filter pairs indicates asaturation value of 98%, then a point in the histogram of FIG. 24 wouldreflect a value of 10 at 98% saturation. This results in a curve similarto the saturation transform curve of FIG. 22. This operation iscompleted in the histogram module 620.

[0334] The results of the histogram provide a power curve similar to thepower curve of FIG. 22. Accordingly, the arterial saturation can becalculated from the histogram by selecting the peak (greatest number ofoccurrences in the area of interest) corresponding to the highestsaturation value (e.g., the peak ‘c’ in Figure peaks corresponding tothe highest saturation value peak. Similarly, the venous or backgroundsaturation can be determined from the histogram by selecting the peakcorresponding to the lowest saturation value (e.g., the peak ‘d’ in FIG.24), in a manner similar to the processing in the saturation calculationmodule 408.

[0335] It should be understood that as an alternative to the histogram,the output saturation (not necessarily a peak in the histogram)corresponding to the highest saturation value could be selected as thearterial saturation with the corresponding ratio representing r_(a).Similarly, the output saturation corresponding to the lowest saturationvalue could be selected as the venous or background saturation with thecorresponding ratio representing r_(v). For example, in this embodiment,the entry ‘a’ in the histogram of FIG. 24 would be chosen as thearterial saturation and the entry in the histogram ‘b’ with the lowestsaturation value would be chosen as the venous or background saturation.

Alternative Determination of Coefficients r_(a) and r_(v)

[0336] As explained above, in accordance with the present invention,primary and secondary signal portions, particularly for pulse oximetry,can be modeled as follows:

S _(red) =s ₁ n ₁(red)  (89)

S _(IR) =s ₂ +n ₂ (infrared)  (90)

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂  (91)

[0337] Substituting Equation (91) into Equation (89) provides thefollowing:

S _(red) =r _(a) s ₂ +r _(v) n ₂ (red)  (92)

[0338] Note that S_(red) and S_(IR) are used in the model of equations(89)-(92). This is because the discussion below is particularly directedto blood oximetry. S_(red) and S_(IR) correspond to S₁ and S₂ in thepreceding text, and the discussion that follows could be generalized forany measure signal S₁ and S₂.

[0339] As explained above, determining r_(a) and r_(v) (which correspondto arterial and venous blood oxygen saturation via a saturationequation) can be accomplished using the saturation transform describedabove doing a scan of many possible coefficients. Another method toobtain r_(a) and r_(v) based on red and infrared data is to look forr_(a) and r_(v) which minimize the correlation between s_(k) and n_(k),assuming s_(k) is at least somewhat (and preferably substantially)uncorrelated with n_(k) (where k=1 or 2). These values can be found byminimizing the following statistical calculation function for k=2:$\begin{matrix}{{Correlation} = {\left( {s_{2},n_{2}} \right) = {{\sum\limits_{i}{{s_{2}\left( {S_{{red}_{i}},{S_{{IR}_{i},}r_{a}},r_{v}} \right)}\quad {n_{2\quad}\left( {S_{{red}_{i}},{S_{{IR}_{i},}r_{a}},r_{v}} \right)}}}}}} & (93)\end{matrix}$

[0340] where i represents time.

[0341] It should be understood that other correlation functions such asa normalized correlation could also be used.

[0342] Minimizing this quantity often provides a unique pair of r_(a)and r_(v) if the noise component is uncorrelated to the desired signalcomponent. Minimizing this quantity can be accomplished by solvingEquations (90) and (92) for s₂ and n₂, and finding the minimum of thecorrelation for possible values of r_(a) and r_(v). Solving for s₂ andn₂ provides the following: $\begin{pmatrix}S_{red} \\S_{IR}\end{pmatrix} = {\begin{pmatrix}r_{a} & r_{v} \\1 & 1\end{pmatrix}\begin{pmatrix}s_{2} \\n_{2}\end{pmatrix}}$

[0343] inverting the two-by-two matrix provides:${Thus},{\begin{pmatrix}r_{a} & r_{v} \\1 & 1\end{pmatrix}^{- 1} = {\frac{1}{r_{a\quad}r_{v}}\begin{pmatrix}1 & {- r_{v}} \\{- 1} & r_{a}\end{pmatrix}}}$ $\begin{pmatrix}s_{2} \\n_{2}\end{pmatrix} = {\frac{1}{r_{a\quad} - r_{v}}\begin{pmatrix}1 & {- r_{v}} \\{- 1} & r_{a}\end{pmatrix}\begin{pmatrix}S_{red} \\S_{IR}\end{pmatrix}}$ or:$s_{2} = {\frac{1}{r_{a\quad} - r_{v}}\left( {s_{red} - {r_{v}s_{IR}}} \right)}$$n_{2} = {\frac{1}{r_{a\quad} - r_{v}}\left( {{- s_{red}} + {r_{a}s_{IR}}} \right)}$

[0344] Preferably, the correlation of equation (93) is enhanced with auser specified window function as follows: $\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {{\sum\limits_{i = 1}^{N}\quad {w_{i}{s_{2}\left( {s_{{red}_{i}},s_{{IR}_{i}},r_{a},r_{v}} \right)}{n_{2}\left( {s_{{red}_{i}},s_{{IR}_{i}},r_{a},r_{v}} \right)}}}}} & \left( {93a} \right)\end{matrix}$

[0345] The Blackman Window is the presently preferred embodiment. Itshould be understood that there are many additional functions whichminimize the correlation between signal and noise. The function above issimply one. Thus, $\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {{\begin{matrix}{\sum\limits_{i = 1}^{N}\quad \left\lbrack {\frac{w_{i}}{\left( {r_{a\quad} - r_{v}} \right)^{2}}\left( {s_{{red}_{i}} - {r_{v}s_{{IR}_{i}}}} \right)} \right.} \\\left. \left( {{- s_{{red}_{i}}} - {r_{a}s_{{IR}_{i}}}} \right) \right\rbrack\end{matrix}}\quad = {\frac{1}{\left( {r_{a\quad} - r_{v}} \right)^{2}}{\begin{matrix}{{- {\sum\limits_{i = 1}^{N}{\left( s_{{red}_{i}} \right)^{2}w_{i}}}} + \left( {r_{a\quad} + r_{v}} \right)} \\{{\sum\limits_{i = 1}^{N}{s_{{IR}_{i}}s_{{red}_{i}}w_{i}}} + {\sum\limits_{i = 1}^{N}{\left( s_{{IR}_{i}} \right)^{2}w_{i}}}}\end{matrix}}}}} & \left( {93b} \right)\end{matrix}$

[0346] In order to implement the minimization on a plurality of discretedata points, the sum of the squares of the red sample points, the sum ofthe squares of the infrared sample points, and the sum of the product ofthe red times the infrared sample points are first calculated (includingthe window function, w_(i)):${RR} = {\sum\limits_{I = 1}^{n}{\left( S_{{red}_{i}} \right)^{2}w_{i}}}$${II} = {\sum\limits_{i = 1}^{n}{\left( S_{{IR}_{i}} \right)^{2}w_{i}}}$${IRR} = {\sum\limits_{i = 1}^{N}{\left( S_{IR} \right)\left( S_{{red}_{i}} \right)w_{i}}}$

[0347] These values are used in the correlation equation (93b). Thus,the correlation equation becomes an equation in terms of two variables,r_(a) and r_(v). To obtain r_(a) and r_(v), an exhaustive scan isexecuted for a good cross-section of possible values for r_(a) and r_(v)(e.g., 20-50 values each corresponding to saturation values ranging from30-105). The minimum of the correlation function is then selected andthe values of r_(a) and r_(v) which resulted in the minimum are chosenas r_(a) and r_(v).

[0348] Once r_(a) and r_(v) have been obtained, arterial oxygensaturation and venous oxygen saturation can be determined by providedr_(a) and r_(v) to a saturation equation, such as the saturationequation 502 of the statistics module 404 which provides an oxygensaturation value corresponding to the ratios r_(a) and r_(v).

[0349] In a further implementation to obtain r_(a) and r_(v), the samesignal model set forth above is again used. In order to determine r_(a)and r_(v) in accordance with this implementation, the energy in thesignal s₂ is maximized under the constraint that s₂ is uncorrelated withn₂. Again, this implementation is based upon minimizing the correlationbetween s and n and on the signal model of the present invention wherethe signal s relates to the arterial pulse and the signal n is the noise(containing information on the venous blood, as well as motion artifactsand other noise); r_(a) is the ratio (RED/IR) related to arterialsaturation and r_(v) is the ratio (RED/IR) related to venous saturation.Accordingly, in this implementation of the present invention, r_(a) andr_(v) are determined such that the energy of the signal s₂ is maximizedwhere s₂ and n₂ are uncorrelated. The energy of the signal s₂ is givenby the following equation: $\begin{matrix}{{{ENERGY}\left( s_{2} \right)} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\quad \left( {s_{red} - {r_{v}s_{IR}}} \right)^{2}}}} & (94) \\{\quad {= {{\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\quad \left( s_{{red}_{i}}^{2} \right)}} - {2r_{v}{\sum\limits_{i = 1}^{N}\quad \left( {s_{{red}_{i}}s_{{IR}_{i}}} \right)}} + {r_{v}^{2}{\sum\limits_{i = 1}^{N}\left( s_{{IR}_{i}}^{2} \right)}}}}} & (95) \\{\quad {= {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {R_{1} - {2r_{v}R_{1,2}} + {r_{v}^{2}R_{2}}} \right\rbrack}}} & (96)\end{matrix}$

[0350] where R₁ is the energy of the red signal, R₂ is the energy of theinfrared signal and R_(1,2) is the correlation between the red andinfrared signals.

[0351] The correlation between s₂ and n₂ is given by $\begin{matrix}{{{Correlation}\quad \left( {s_{2},n_{2}} \right)} = {{\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\quad {\left( {S_{{red}_{i}} - {r_{v}S_{{ir}_{i}}}} \right)\left( {{- S_{{red}_{i}}} - {r_{a}S_{{IR}_{i}}}} \right)}}}\quad = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {{- R_{1}} + {\left( {r_{a} + r_{v}} \right)R_{1,2}} - {r_{v}r_{a}R_{2}}} \right\rbrack}}} & (97)\end{matrix}$

[0352] As explained above, the constraint is that s_(k) and n_(k) (k=2for the present example) are uncorrelated. This “decorrelationconstraint” is obtained by setting the correlation of Equation (97) tozero as follows:

−R ₁+(r _(a) +r _(v))R ₁₂ −r _(a) r _(v) R ₂=0  (98)

[0353] In other words, the goal is to maximize equation (94) under theconstraint of equation (98).

[0354] In order to obtain the goal, a cost function is defined (e.g., aLagrangian optimization in the present embodiment) as follows:$\begin{matrix}{{J\left( {r_{a},r_{v},\mu} \right)} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {R_{1} - {2r_{v}R_{1,2}} + {r_{v}^{2}R_{2}} + {\mu \left( {{- R_{1}} + {\left( {r_{a} + r_{v}} \right)R_{1,2}} - {r_{a}r_{v}R_{2}}} \right)}} \right\rbrack}} & (99)\end{matrix}$

[0355] where μ is the Lagrange multiplier. Finding the value of r_(a),r_(v) and μ that solve the cost function can be accomplished using aconstrained optimization method such as described in Luenberger, Linear& Nonlinear Programming, Addison-Wesley, 2d Ed., 1984.

[0356] Along the same lines, if we assume that the red and infraredsignals S_(red) and S_(IR) are non-static, the functions R₁, R₂ and R₁₂defined above are time dependent. Accordingly, with two equations, twounknowns can be obtained by expressing the decorrelation constraint setforth in equation (98) at two different times. The decorrelationconstraint can be expressed at two different times, t₁ and t₂, asfollows:

−R ₁(t ₁)+(r _(a) +r _(v))R ₁₂(t ₁)−r _(a) r _(v) R ₂(t)=0  (100)

−R ₁(t ₂)+(r _(a) +r _(v))R ₁₂(t ₂)−r _(a) r _(v) R ₂(t ₂)=0  (101)

[0357] Because equations (100) and (101) are non-linear in r_(a) andr_(v), a change of variables allows the use of linear techniques tosolve these two equations. Accordingly, with x=r_(a)+r_(v); y=r_(a)r_(v)equations (100) and (101) become

R ₁₂(t ₁)x−R ₂(t ₁)y=R ₁(t ₁)  (102)

R ₁₂(t ₂)x−R ₂(t ₂)y=R ₁(t ₂)  (103)

[0358] These equation (102) and (103) can be solved for x and y. Then,solving for r_(a) and r_(v) from the changes of variables equationsprovides the following: $\begin{matrix}{{r_{v} + \frac{y}{r_{v}}} = {x = {{\succ {r_{v}^{2} - {x\quad r_{v}} + y}} = 0}}} & (104)\end{matrix}$

[0359] Solving equation (104) results in two values for r_(v). In thepresent embodiment, the r_(v) value that results in x²−r_(v)y>0 isselected. If both values of r_(v) result in x²−r_(v)y>0, the r_(v) thatmaximizes the energy of s₂ (Energy(s₂)) at t₂ is selected. r_(v) is thensubstituted into the equations above to obtain r_(a). Alternativelyr_(a) can be found directly in the same manner r_(v) was determined.

[0360] Alternative To Saturation Transform—Complex FFT

[0361] The blood oxygen saturation, pulse rate and a cleanplethysmographic waveform of a patient can also be obtained using thesignal model of the present invention using a complex FFT, as explainedfurther with reference to FIGS. 25A-25C. In general, by utilizing thesignal model of equations (89)-(92) with two measured signals, each witha first portion and a second portion, where the first portion representsa desired portion of the signal and the second portion represents theundesired portion of the signal, and where the measured signals can becorrelated with coefficients r_(a) and r_(v), a fast saturationtransform on a discrete basis can be used on the sample points from theoutput of the decimation operation 402.

[0362]FIG. 25A corresponds generally to FIG. 14, with the fastsaturation transform replacing the previously described saturationtransform. In other words, the operations of FIG. 25A can replace theoperations of FIG. 14. As depicted in FIG. 25A, the fast saturationtransform is represented in a fast saturation transform/pulse ratecalculation module 630. As in FIG. 14, the outputs are arterial oxygensaturation, a clean plethysmographic waveform, and pulse rate. FIGS. 25Band 25C illustrate additional detail regarding the fast saturationtransform/pulse rate calculation module 630. As depicted in FIG. 25B,the fast saturation transform module 630 has infrared log and red logmodules 640, 642 to perform a log normalization as in the infrared andred log modules 480, 482 of FIG. 17. Similarly, there are infrared DCremoval and red DC removal modules 644, 646. In addition, there areinfrared and red high-pass filter modules 645, 647, window functionmodules 648, 640, complex FFT modules 652, 654, select modules 653, 655,magnitude modules 656, 658, threshold modules 660, 662, a point-by-pointratio module 670, a saturation equation module 672, and a selectsaturation module 680. There are also phase modules 690, 692, a phasedifference module 694, and a phase threshold module 696. The output ofthe select saturation module 680 provides the arterial saturation anarterial saturation output line 682.

[0363] In this alternative embodiment, the snapshot for red and infraredsignals is 562 samples from the decimation module 402. The infrared DCremoval module 644 and the red DC removal module 646 are slightlydifferent from the infrared and red DC removal modules 484, 486 of FIG.17. In the infrared and red DC removal modules 644, 646 of FIG. 25B, themean of all 563 sample points for each respective channel is calculated.This mean is then removed from each individual sample point in therespective snapshot in order to remove the baseline DC from each sample.The outputs of the infrared and red DC removal modules 644, 646 provideinputs to respective infrared high-pass filter module 645 and redhigh-pass filter module 647.

[0364] The high-pass filter modules 645, 647 comprise FIR filters with51 taps for coefficients. Preferably, the high-pass filters compriseChebychev filters with a side-lobe level parameter of 30 and a cornerfrequency of 0.5 Hz (i.e., 30 beats/minute). It will be understood thatthis filter could be varied for performance. With 562 sample pointsentering the high-pass filters, and with 51 taps for coefficients, thereare 512 samples provided from these respective infrared and redsnapshots at the output of the high-pass filter modules. The output ofthe high-pass filter modules provides an input to the window functionmodules 648, 650 for each respective channel.

[0365] The window function modules 648, 650 perform a conventionalwindowing function. A Kaiser windowing function is used in the presentembodiment. The functions throughout FIG. 25B maintain a point-by-pointanalysis. In the present embodiment, the time bandwidth product for theKaiser window function is 7. The output of the window function modulesprovides an input to the respective complex Fast Fourier Transform (FFT)modules 652, 654.

[0366] The complex FFT modules 652, 654 perform complex FFTs onrespective infrared and red channels on the data snapshots. The datafrom the complex FFTs is then analyzed in two paths, once which examinesthe magnitude and one which examines the phase from the complex FFT datapoints. However, prior to further processing, the data is provided torespective infrared and red select modules 653, 655 because the outputof the FFT operation will provide repetitive information from 0-½ thesampling rate and from ½ the sampling rate to the sampling rate. Theselect modules select only samples from 0-½ the sampling rate (e.g.,0-31.25 Hz in the present embodiment) and then select from those samplesto cover a frequency range of the heart rate and one or more harmonicsof the heart rate. In the present embodiment, samples which fall in thefrequency range of 20 beats per minute to 500 beats per minute areselected. This value can be varied in order to obtain harmonics of theheart rate as desired. Accordingly, the output of the select modulesresults in less than 256 samples. In the present embodiment, the samplepoints 2-68 of the outputs of the FFTs are utilized for furtherprocessing.

[0367] In the first path of processing, the output from the selectmodules 653, 655 are provided to respective infrared and red magnitudemodules 656, 658. The magnitude modules 656, 658 perform a magnitudefunction wherein the magnitude on a point-by-point basis of the complexFFT points is selected for each of the respective channels. The outputsof the magnitude modules 656, 658 provide an input to infrared and redthreshold modules 660, 662.

[0368] The threshold modules 660, 662 examine the sample points, on apoint-by-point basis, to select those points where the magnitude of anindividual point is above a particular threshold which is set at apercentage of the maximum magnitude detected among all the remainingpoints in the snapshots. In the present embodiment, the percentage forthe threshold operation is selected as 1% of the maximum magnitude.

[0369] After thresholding, the data points are forwarded to apoint-by-point ratio module 670. The point-by-point ratio module takesthe red over infrared ratio of the values on a point-by-point basis.However, a further test is performed to qualify the points for which aratio is taken. As seen in FIG. 25B, the sample points output from theselect modules 653, 655 are also provided to infrared and red phasemodules 690, 692. The phase modules 690, 692 select the phase value fromthe complex FFT points. The output of the phase modules 690, 692 is thenpresented to a phase difference module 694.

[0370] The phase difference module 694 calculates the difference inphase between the corresponding data points from the phase modules 690,692. If the magnitude of the phase difference between any twocorresponding points is less than a particular threshold (e.g., 0.1radians) in the present embodiment), then the sample points qualify. Ifthe phase of two corresponding sample points is too far apart, then thesample points are not used. The output of the phase threshold module 696provides an enable input to the RED/IR rate module 670. Accordingly, inorder for the ratio of a particular pair of sample points to be taken,the three tests are executed:

[0371] 1. the red sample must pass the red threshold 660;

[0372] 2. the infrared sample must pass the infrared threshold 662; and

[0373] 3. the phase between the two points must be less than thepredefined threshold as determined in the phase threshold 696.

[0374] For those sample points which qualify, a ratio is taken in theratio module 670. For those points which do not qualify, the saturationis set to zero at the output of the saturation equation 672.

[0375] The resulting ratios are provided to a saturation equation modulewhich is the same as the saturation equation modules 502, 520 in thestatistics module 504. In other words, the saturation equation module672 accepts the ratio on a point-by-point basis and provides as anoutput a corresponding saturation value corresponding to the discreteratio points. The saturation points output from the saturation equationmodule 672 provide a series of saturation points which could be plottedas saturation with respect to frequency. The frequency reference wasentered into the points at the complex FFT stage.

[0376] The arterial (and the venous) saturation can then be selected, asrepresented in the select arterial saturation module 680, in one of twomethods according to the present invention. According to one method, thearterial saturation value can be selected simply as the pointcorresponding to the largest saturation value for all points output fromthe saturation equation module 672 for a packet. Alternatively, ahistogram similar to the histogram of FIG. 22 can be generated in whichthe number of saturation values at different frequencies (points) aresummed to form a histogram of the number of occurrences for eachparticular saturation value. In either method, the arterial saturationcan be obtained and provided as an output to the select arterialsaturation module on the arterial saturation output line 682. In orderto obtain the venous saturation, the minimum arterial saturation value,of points that exhibit non-zero value, is selected rather than themaximum arterial saturation value. The saturation can be provided to thedisplay 336.

[0377] The fast saturation transform information can also be used toprovide the pulse rate and the clean plethysmographic wave form asfurther illustrated in FIG. 25C. In order to obtain the pulse rate and aclean plethysmographic wave form, several additional functions arenecessary. As seen in FIG. 25C, the pulse rate and cleanplethysmographic wave form are determined using a window function module700, a spectrum analysis module 702 and an inverse window functionmodule 704.

[0378] As depicted in FIG. 25C, the input to the window function module700 is obtained from the output of the complex FFT modules 652 or 654.In the present embodiment, only one measured signal is necessary.Another input to the window function module 700 is the arterialsaturation obtained from the output of the select arterial saturationmodule 680.

[0379] The window function module performs a windowing function selectedto pass those frequencies that significantly correlate to thefrequencies which exhibited saturation values very close to the arterialsaturation value. In the present embodiment, the following windowingfunction is selected: $\begin{matrix}{1 - \left\lbrack \frac{{SAT}_{art} - {SAT}_{n}}{100} \right\rbrack^{15}} & (105)\end{matrix}$

[0380] where SAT_(n) equals the saturation value corresponding to eachparticular frequency for the sample points and SAT_(art) represents thearterial saturation as chosen at the output of the select arterialsaturation module 680. This window function is applied to the windowfunction input representing the complex FFT of either the red or theinfrared signal. The output of the window function module 700 is a redor infrared signal represented with a frequency spectrum as determinedby the FFT, with motion artifacts removed by the windowing function. Itshould be understood that many possible window functions can beprovided. In addition, with the window function described above, itshould be understood that using a higher power will provide more noisesuppression.

[0381] In order to obtain pulse rate, the output points from the windowfunction module 700 are provided to a spectrum analysis module 702. Thespectrum analysis module 702 is the same as the spectrum analysis module590 of FIG. 20. In other words, the spectrum analysis module 702determines the pulse rate by determining the first harmonic in thefrequency spectrum represented by the output points of the windowingfunction 700. The output of spectrum analysis module 702 is the pulserate.

[0382] In order to obtain a clean plethysmographic waveform, the outputof the windowing function 700 is applied to an inverse window functionmodule 794. The inverse window function module 704 completes an inverseof the Kaiser window function of the window function module 648 or 650of FIG. 25B. In other words, the inverse window function 704 does apoint-by-point inverse of the Kaiser function for points that are stilldefined. The output is a clean plethysmographic waveform.

[0383] Accordingly, by using a complex FFT and windowing functions, thenoise can be suppressed from the plethysmographic waveform in order toobtain the arterial saturation, the pulse rate, and a cleanplethysmographic waveform. It should be understood that although theabove description relates to operations primarily in the frequencydomain, operations that obtain similar results could also beaccomplished in the time domain.

[0384] Relation to Generalized Equations

[0385] The measurements described for pulse oximetry above are nowrelated back to the more generalized discussion above. The signals(logarithm converted) transmitted through the finger 310 at eachwavelength λa and λb are:

S _(λa)(t)=S _(λred1)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λa) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λa) c^(V) _(Hb) x ^(V)(t)+n _(λa)(t);  (105a)

S _(λa)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa) c ^(A) _(Hb) x^(A)(t)+n _(λa)(t);  (105b)

S _(λa)(t)=s _(λa)(t)+n _(λa)(t);  (105c)

S _(λb)(t)=S _(λred2)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λb) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λb) c^(V) _(Hb) x ^(V)(t)+n _(λb)(t);  (106a)

S _(λb)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb) c ^(A) _(Hb) x^(A)(t)+n _(λb)(t)  (106b)

S _(λb)(t)=s _(λb)(t)+n _(λb)(t)  (106c)

[0386] The variables above are best understood as correlated to FIG. 6cas follows: assume the layer in FIG. 6c containing A₃ and A₄ representsvenous blood in the test medium, with A₃ representing deoxygenatedhemoglobin (Hb) and A₄ representing oxygenated hemoglobin (HBO2) in thevenous blood. Similarly, assume that the layer in FIG. 6c containing A₅and A₆ represents arterial blood in the test medium, with A₅representing deoxygenated hemoglobin (Hb) and A₆ representing oxygenatedhemoglobin (HBO2) in the arterial blood. Accordingly, c^(V)HbO2represents the concentration of oxygenated hemoglobin in the venousblood, c^(V)Hb represents the concentration of deoxygenated hemoglobinin the venous blood, x^(V) represents the thickness of the venous blood(e.g. the thickness the layer containing A₃ and A₄). Similarly,c^(A)HbO2 represents the concentration of oxygenated hemoglobin in thearterial blood, cAHb represents the concentration of deoxygenatedhemoglobin in the arterial blood, and xA represents the thickness of thearterial blood (e.g., the thickness of the layer containing A₅ and A₆)

[0387] The wavelengths chosen are typically one in the visible redrange, i.e., λa, and one in the infrared range, i.e., λb. Typicalwavelength values chosen are λa=660 nm and λb=910 nm. In accordance withthe constant saturation method, it is assumed that cA _(HbO2)(t)/c^(A)_(Hb)(t)=constant₁ and c^(V) _(HbO2)(t)/c^(V) _(Hb)(t)=constant₂. Theoxygen saturation of arterial and venous blood changes slowly, if atall, with respect to the sample rate, making this a valid assumption.The proportionality coefficients for equations (105) and (106) can thenbe written as: $\begin{matrix}{{r_{a}(t)} = {\frac{\in_{{Hb02},{\lambda \quad a}}{{c_{Hb02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \quad a}}{c_{Hb}{x(t)}}}{\in_{{Hb02},{\lambda \quad b}}{{c_{Hb02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \quad b}}{C_{Hb}^{A}{x(t)}}}*}} & (107)\end{matrix}$

 s _(λa)(t)=r _(a)(t)s _(λb)(t)  (108a)

n _(λa)(t)≠r _(a)(t)n _(λb)(t)  (109a)

n _(λa)(t)=r _(v)(t)n _(λb)(t)  (108b)

s _(λa)(t)≠r _(v)(t)s _(λb)(t)  (109b)

[0388] In pulse oximetry, it is typically the case that both equations(108) and

[0389] (109) can be satisfied simultaneously.

[0390] Multiplying equation (106) by r_(a)(t) and then subtractingequation (106) from equation (105), a non-zero secondary referencesignal n′(t) is determined by: $\begin{matrix}{{{n'}(t)} = {{S_{\lambda \quad a}(t)} - {{r_{a}(t)}{S_{\lambda \quad b}(t)}}}} & \left( {110a} \right) \\{\quad {= {{ɛ_{{H\quad {bO2}},{\lambda \quad a}}c_{H\quad {bO2}}^{V}{x^{V}(t)}} + {ɛ_{{H\quad b},{\lambda \quad a}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \quad a}(t)} - \quad {{r_{a}(t)}\left\lbrack {{ɛ_{{H\quad {bO2}},{\lambda \quad b}}c_{HbO2}^{V}{x^{V}(t)}} + {{ɛ_{H\quad b}}_{,{\lambda \quad b}}c_{H\quad b}^{V}{x^{V}(t)}} + {n_{\lambda \quad b}(t)}} \right\rbrack}}}} & \left( {111a} \right)\end{matrix}$

[0391] Multiplying equation (106) by r_(v)(t) and then subtractingequation (106) from equation (105), a non-zero primary reference signals′(t) is determined by: $\begin{matrix}{{s^{\prime}(t)} = {{S_{\lambda \quad a}(t)} - {{r_{v}(t)}{S_{\lambda \quad b}(t)}}}} & \left( {110b} \right) \\{\quad {= {{s_{\lambda \quad a}(t)} - {{r_{v}(t)}{s_{\lambda \quad b}(t)}}}}} & \left( {111b} \right)\end{matrix}$

[0392] The constant saturation assumption does not cause the venouscontribution to the absorption to be canceled along with the primarysignal portions s_(λa)(t) and s_(λb)(t). Thus, frequencies associatedwith both the low frequency modulated absorption due to venousabsorption when the patient is still and the modulated absorption due tovenous absorption when the patient is moving are represented in thesecondary reference signal n′(t). Thus, the correlation canceler orother methods described above remove or derive both erraticallymodulated absorption due to venous blood in the finger under motion andthe constant low frequency cyclic absorption of venous blood.

[0393] To illustrate the operation of the oximeter of FIG. 11 to obtainclean waveform, FIGS. 26 and 27 depict signals measured for input to areference processor of the present invention which employs the constantsaturation method, i.e., the signals S_(λa)(t)=S_(λred)(t) andS_(λb)(t)=S_(IR)(t). A first segment 26 a and 27 a of each of thesignals is relatively undisturbed by motion artifact, i.e., the patientdid not move substantially during the time period in which thesesegments were measured. These segments 26 a and 27 a are thus generallyrepresentative of the primary plethysmographic waveform at each of themeasured wavelengths. A second segment 26 b and 27 b of each of thesignals is affected by motion artifact, i.e., the patient did moveduring the time period in which these segments were measured. Each ofthese segments 26 b and 27 b shows large motion induced excursions inthe measured signal. A third segment 26 c and 27 c of each of thesignals is again relatively unaffected by motion artifact and is thusgenerally representative of the primary plethysmographic waveform ateach of the measured wavelengths.

[0394]FIG. 28 shows the secondary reference signaln′(t)=n_(λa)(t)−r_(a)n_(λb)(t), as determined by a reference processorof the present invention. Again, the secondary reference signal n′(t) iscorrelated to the secondary signal portions n_(a) and n_(b). Thus, afirst segment 28 a of the secondary reference signal n′(t) is generallyflat, corresponding to the fact that there is very little motion inducednoise in the first segments 26 a and 27 a of each signal. A secondsegment 28 b of the secondary reference signal n′(t) exhibits largeexcursions, corresponding to the large motion induced excursions in eachof the measured signals. A third segment 28 c of the noise referencesignal n′(t) is generally flat, again corresponding to the lack ofmotion artifact in the third segments 26 c and 27 c of each measuredsignal.

[0395] It should also be understood that a reference processor could beutilized in order to obtain the primary reference signals′(t)=s_(λa)−r_(v)s_(λb)(t). The primary reference signal s′(t) would begenerally indicative of the plethysmograph waveform.

[0396]FIGS. 29 and 30 show the approximation s″_(λa)(t) and s″_(λb)(t)to the primary signals s_(λa)(t) and s_(λb)(t) as estimated by acorrelation canceler using a secondary reference signal n′(t). Note thatthe scale of FIGS. 26 through 30 is not the same for each figure tobetter illustrate changes in each signal. FIGS. 29 and 30 illustrate theeffect of correlation cancellation using the secondary reference signaln′(t) as determined by the reference processor. Segments 29 b and 30 bare not dominated by motion induced noise as were segments 26 b and 27 bof the measured signals. Additionally, segments 29 a, 30 a, 29 c, and 30c have not been substantially changed from the measured signal segments26 a, 27 a, 26 c, and 27 c where there was no motion induced noise.

[0397] It should be understood that approximation n″_(λa)(t) andn″_(λb)(t) to the secondary signals n_(λa)(t) and n_(λb)(t) as estimatedby a correlation canceler using a primary reference signal s′(t) canalso be determined in accordance with the present invention.

Method for Estimating Primary and Secondary Signal Portions of MeasuredSignals in a Pulse Oximeter

[0398] Implementing the various embodiments of the correlation cancelerdescribed above in software is relatively straightforward given theequations set forth above, and the detailed description above. However,a copy of a computer program subroutine, written in the C programminglanguage, which calculates a primary reference s′(t) using the constantsaturation method and, using a joint process estimator 572 whichimplements a joint process estimator using the equations (54)-(64) isset forth in Appendix B. This joint process estimator estimates a goodapproximation to the primary signal portions of two measured signals,each having a primary portion which is correlated to the primaryreference signal s′(t) and a secondary portion which is correlated tothe secondary reference signal n′(t). This subroutine is another way toimplement the steps illustrated in the flowchart of FIG. 9 for a monitorparticularly adapted for pulse oximetry. The two signals are measured attwo different wavelengths λa and λb, where λa is typically in thevisible region and λb is typically in the infrared region. For example,in one embodiment of the present invention, tailored specifically toperform pulse oximetry using the constant saturation method, Na=660 nmand b=940 nm.

[0399] The correspondence of the program variables to the variablesdefined in equations (54)-(64) in the discussion of the joint processestimator is as follows:

Δ_(m)(t)=nc[m].Delta

Γ_(f,m)(t)=nc[m].fref

Γ_(b,m)(t)=nc[m].bref

f _(m)(t)=nc[m].ferr

b _(m)(t)=nc[m].berr

ℑ_(m)(t)=nc[m].Fswsqr

β_(m)(t)=nc[m].Bswsqr

γ_(m)(t)=nc[m].Gamma

ρ_(m,λa)(t)=nc[m].Roh _(—) a

ρ_(m,λb)(t)=nc[m].Roh _(—) b

e _(m,λa)(t)=nc[m].err _(—) a

e _(m,λb)(t)=nc[m].err _(—) b

κ_(m,λa)(t)=nc[m].K _(—) a

κ_(m,λb)(t)=nc[m].K _(—) b

[0400] A first portion of the program performs the initialization of theregisters 90, 92, 96, and 98 and intermediate variable values as in the“INITIALIZED CORRELATION CANCELER” action block 120. A second portion ofthe program performs the time updates of the delay element variables 110with the value at the input of each delay element variable 110 is storedin the delay element variable 110 as in the “TIME UPDATE OF LEFT [Z⁻¹]ELEMENTS” action block 130. The calculation of saturation is performedin a separate module. Various methods for calculation of the oxygensaturation are known to those skilled in the art. One such calculationis described in the articles by G. A. Mook, et al, and Michael R. Neumancited above. Once the concentration of oxygenated hemoglobin anddeoxygenated hemoglobin are determined, the value of the saturation isdetermined similarly to equations (72) through (79) wherein measurementsat times t₁ and t₂ are made at different, yet proximate times over whichthe saturation is relatively constant. For pulse oximetry, the averagesaturation at time t=(t₁+t₂)/2 is then determined by: $\begin{matrix}{{{Sat}_{arterial}(t)} = \frac{C_{H\quad {b02}}^{A}(t)}{{C_{H\quad {b02}}^{A}(t)} + {C_{H\quad b}^{A}(t)}}} & \left( {112a} \right) \\{\quad {= \frac{\in_{{H\quad b},{\lambda \quad a}}{- {\in_{{Hb},{\lambda \quad b}}\left( {\Delta \quad {S_{\lambda \quad a}/\Delta}\quad S_{\lambda \quad b}} \right)}}}{\in_{{HB},{\lambda \quad a}}{- {\in_{{Hb02},{\lambda \quad a}}{{- \left( {\in_{{HB},{\lambda \quad b}}{- \in_{{Hb02},{\lambda \quad b}}}} \right)}\left( {\Delta \quad {S_{\lambda \quad a}/\Delta}\quad S_{\lambda \quad b}} \right)}}}}}} & \left( {112b} \right) \\{{{Sat}_{venous}(t)} = \frac{C_{H\quad {b02}}^{V}(t)}{{C_{H\quad {b02}}^{V}(t)} + {C_{H\quad b}^{V}(t)}}} & \left( {113a} \right) \\{\quad {= \frac{\in_{{H\quad b},{\lambda \quad a}}{- {\in_{{Hb},{\lambda \quad b}}\left( {\Delta \quad {n_{\lambda \quad a}/\Delta}\quad n_{\lambda \quad b}} \right)}}}{\in_{{HB},{\lambda \quad a}}{- {\in_{{Hb02},{\lambda \quad a}}{{- \left( {\in_{{HB},{\lambda \quad b}}{- \in_{{Hb02},{\lambda \quad b}}}} \right)}\left( {\Delta \quad {n_{\lambda \quad a}/\Delta}\quad n_{\lambda \quad b}} \right)}}}}}} & \left( {113b} \right)\end{matrix}$

[0401] A third portion of the subroutine calculates the primaryreference or secondary reference, as in the “CALCULATE PRIMARY ORSECONDARY REFERENCE (s′(t) or n′(t)) FOR TWO MEASURED SIGNAL SAMPLES”action block 140 for the signals S_(λa)(t) and S_(λb)(t) using theproportionality constants r_(a)(t) and r_(v)(t) determined by theconstant saturation method as in equation (3). The saturation iscalculated in a separate subroutine and a value of r_(a)(t) or r_(v)(t)is imported to the present subroutine for estimating either the primaryportions s_(λa)(t) and s_(λb)(t) or the secondary portions n_(λa)(t) andn_(λb)(t) of the composite measured signals S_(λa)(t) and S_(λb)(t).

[0402] A fourth portion of the program performs Z-stage update as in the“ZERO STAGE UPDATE” action block 150 where the Z-stage forwardprediction error F_(o)(t) and Z-stage backward prediction error b_(o)(t)are set equal to the value of the reference signal n′(t) or s′(t) justcalculated. Additionally zero-stage values of intermediate variablesℑ_(o) and β₀(t)(nc[m].Fswsqr and nc[m].Bswsqr in the program) arecalculated for use in setting registers 90, 92, 96, and 98 values in theleast-squares lattice predictor 70 in the regression filters 80 a and 80b.

[0403] A fifth portion of the program is an iterative loop wherein theloop counter, M, is reset to zero with a maximum of m=NC_CELLS, as inthe “m=0” action block 160 in FIG. 9. NC_CELLS is a predeterminedmaximum value of iterations for the loop. A typical value for NC_CELLSis between 6 and 10, for example. The conditions of the loop are setsuch that the loop iterates a minimum of five times and continues toiterate until a test for conversion is met or m-NC_CELLS. The test forconversion is whether or not the sum of the weighted sum of fourprediction errors plus the weighted sum of backward prediction errors isless than a small number, typically 0.00001 (i.e.,ℑ_(m)(t)+βm(t)≦0.00001).

[0404] A sixth portion of the program calculates the forward andbackward reflection coefficient Γ_(m,f)(t) and Γ_(m,b)(t) register 90and 92 values (nc[m].fref and nc[m].bref in the program) as in the“ORDER UPDATE m^(th)-STAGE OF LSL-PREDICTOR” action block 170. Thenforward and backward prediction errors f_(m)(t) and b_(m)(t) (nc[m].ferrand nc[m].berr in the program) are calculated. Additionally,intermediate variables ℑ_(m)(t), β_(m)(t), and γ(t) (nc[m].Fswsqr,nc[m].Bswsqr, nc[m]. gamma in the program) are calculated. The firstcycle of the loop uses the value for nc[0].Fswsqr and nc[0].Bswsqrcalculated in the ZERO STAGE UPDATE portion of the program.

[0405] A seventh portion of the program, still within the loop begun inthe fifth portion of the program, calculates the regression coefficientregister 96 and 98 values κ_(m,λa)(t) and κ_(m,λb)(t) (nc[m].K_a andnc[m].K_b in the program) in both regression filters, as in the “ORDERUPDATE m^(th) STAGE OF REGRESSION FILTER(S)” action block 180.Intermediate error signals and variables e_(m,λa)(t), e_(m,λb)(t),ρ_(m,λa)(t), and p_(m,λb)(t) (nc[m].err_a and nc[m].err_b, nc[m].roh_a,and nc[m].roh_b in the subroutine) are also calculated.

[0406] The loop iterates until the test for convergence is passed. Thetest for convergence of the joint process estimator is performed eachtime the loop iterates analogously to the “DONE” action block 190. Ifthe sum of the weighted sums of the forward and backward predictionerrors ℑ_(m)(t)+β_(m)(t) is less than or equal to 0.00001, the loopterminates. Otherwise, sixth and seventh portions of the program repeat.

[0407] The output of the present subroutine is a good approximation tothe primary signals s″_(λa)(t) and s″_(λb)(t) or the secondary signalsn″_(λa)(t) and n″_(λb)(t) for the set of samples S_(λa)(t) and S_(λb)(t)input to the program. After approximations to the primary signalportions or the secondary signals portions of many sets of measuredsignal samples are estimated by the joint process estimator, acompilation of the outputs provides waves which are good approximationsto the plethysmographic wave or motion artifact at each wavelength, λaand λb.

[0408] It should be understood that the subroutine of Appendix B ismerely one embodiment which implements the equations (54)-(64). Althoughimplementation of the normalized and QRD-LSL equations is alsostraightforward, a subroutine for the normalized equations is attachedas Appendix C, and a subroutine for the QRD-LSL algorithm is attached asAppendix D.

[0409] While one embodiment of a physiological monitor incorporating aprocessor of the present invention for determining a reference signalfor use in a correlation canceler, such as an adaptive noise canceler,to remove or derive primary and secondary components from aphysiological measurement has been described in the form of a pulseoximeter, it will be obvious to one skilled in the art that other typesof physiological monitors may also employ the above describedtechniques.

[0410] Furthermore, the signal processing techniques described in thepresent invention may be used to compute the arterial and venous bloodoxygen saturations of a physiological system on a continuous or nearlycontinuous time basis. These calculations may be performed, regardlessof whether or not the physiological system undergoes voluntary motion.

[0411] Furthermore, it will be understood that transformations ofmeasured signals other than logarithmic conversion and determination ofa proportionality factor which allows removal or derivation of theprimary or secondary signal portions for determination of a referencesignal are possible. Additionally, although the proportionality factor rhas been described herein as a ratio of a portion of a first signal to aportion of a second signal, a similar proportionality constantdetermined as a ratio of a portion of a second signal to a portion of afirst signal could equally well be utilized in the processor of thepresent invention. In the latter case, a secondary reference signalwould generally resemble n′(t)=n_(λb)(t)−rn_(λa)(t).

[0412] Furthermore, it will be understood that correlation cancellationtechniques other than joint process estimation may be used together withthe reference signals of the present invention. These may include butare not limited to least mean square algorithms, wavelet transforms,spectral estimation techniques, neural networks, Weiner and Kalmanfilters among others.

[0413] One skilled in the art will realize that many different types ofphysiological monitors may employ the teachings of the presentinvention. Other types of physiological monitors include, but are in notlimited to, electro cardiographs, blood pressure monitors, bloodconstituent monitors (other than oxygen saturation) monitors,capnographs, heart rate monitors, respiration monitors, or depth ofanesthesia monitors. Additionally, monitors which measure the pressureand quantity of a substance within the body such as a breathalizer, adrug monitor, a cholesterol monitor, a glucose monitor, a carbon dioxidemonitor, a glucose monitor, or a carbon monoxide monitor may also employthe above described techniques.

[0414] Furthermore, one skilled in the art will realize that the abovedescribed techniques of primary or secondary signal removal orderivation from a composite signal including both primary and secondarycomponents can also be performed on electrocardiography (ECG) signalswhich are derived from positions on the body which are close and highlycorrelated to each other. It should be understood that a tripolarLaplacian electrode sensor such as that depicted in FIG. 31 which is amodification of a bipolar Laplacian electrode sensor discussed in thearticle “Body Surface Laplacian ECG Mapping” by Bin He and Richard J.Cohen contained in the journal IEEE Transactions on BiomedicalEngineering, Vol. 39, No. 11, November 1992 could be used as an ECGsensor. It must also be understood that there are a myriad of possibleECG sensor geometry's that may be used to satisfy the requirements ofthe present invention. The same type of sensor could also be used forEEG and EMG measurements.

[0415] Furthermore, one skilled in the art will realize that the abovedescribed techniques can also be performed on signals made up ofreflected energy, rather than transmitted energy. One skilled in the artwill also realize that a primary or secondary portion of a measuredsignal of any type of energy, including but not limited to sound energy,X-ray energy, gamma ray energy, or light energy can be estimated by thetechniques described above. Thus, one skilled in the art will realizethat the techniques of the present invention can be applied in suchmonitors as those using ultrasound where a signal is transmitted througha portion of the body and reflected back from within the body backthrough this portion of the body. Additionally, monitors such as echocardiographs may also utilize the techniques of the present inventionsince they too rely on transmission and reflection.

[0416] While the present invention has been described in terms of aphysiological monitor, one skilled in the art will realize that thesignal processing techniques of the present invention can be applied inmany areas, including but not limited to the processing of aphysiological signal. The present invention may be applied in anysituation where a signal processor comprising a detector receives afirst signal which includes a first primary signal portion and a firstsecondary signal portion and a second signal which includes a secondprimary signal portion and a second secondary signal portion. Thus, thesignal processor of the present invention is readily applicable tonumerous signal processing areas.

What is claimed is:
 1. A method of determining a pulse rate of a patientusing a patient monitoring device that includes a non-invasive opticalprobe and signal processing components capable of processing signalsreceived from the non-invasive optical probe and capable of determiningthe pulse rate, the method comprising: receiving physiological signalsrepresentative of attenuation of light of at least first and secondwavelengths by body tissue carrying pulsing blood; determining at leasttwo values corresponding to pulse rate based upon at least twoalternative methods of processing the physiological signals; anddetermining a resulting value for pulse rate from the at least twovalues corresponding to pulse rate.
 2. The method of claim 1, whereindetermining the resulting value comprises selecting at least one of theat least two values based on a determination of confidence in theaccuracy of physiological signals.
 3. The method of claim 1, whereindetermining the resulting value comprises averaging the at least twovalues.
 4. The method of claim 3, wherein the averaging comprisesaveraging over a time window, wherein the time window is increased whenthe at least two values are associated with a lower confidence ofaccuracy and the time window is decreased when the at least two valuesare associated with a higher confidence of accuracy.
 5. A method ofdetermining a pulse rate of pulsing blood, the method comprising:receiving first and second intensity signals from a light-sensitivedetector which detects light of at least first and second wavelengthsattenuated by body tissue carrying pulsing blood; providing at leastfirst and second calculation techniques, wherein each calculationtechnique is capable of generating at least one value representative ofthe, pulse rate of the pulsing blood based on at least one of the firstand second intensity signals; and utilizing at least one of the firstand second calculation techniques to electronically determine aresulting value indicative of the pulse rate.
 6. A method of determiningblood pulse rate, the method comprising: receiving first and secondintensity signals from a light-sensitive detector which detects light ofat least first and second wavelengths attenuated by body tissue carryingpulsing blood, wherein the first and second intensity signals are atleast partially based on a pulse of the pulsing blood; transforming thefirst and second intensity signals into first and second sets ofspectral domain data; and determining a pulse rate of the pulsing bloodbased on more than one indication of the pulse rate from the first andsecond sets of spectral domain data.
 7. The method of claim 6, whereinthe first and second intensity signals include motion induced noise. 8.The method of claim 6, wherein at least one of the first and second setsof spectral domain data comprises frequency domain data.
 9. The methodof claim 6, wherein at least one of the indications of the pulse ratecomprises information gained by reviewing peaks in at least one of thefirst and second sets of spectral domain data.
 10. The method of claim6, wherein at least one of the indications of the pulse rate compriseinformation gained by comparing phase information from the first andsecond sets of spectral domain data.
 11. The method of claim 6, whereinone of the more than one indications of the pulse rate comprisesinformation gained by reviewing harmonics in at least one of the firstand second sets of spectral domain data.
 12. The method of claim 6,wherein the more than one indications of the pulse rate comprise ratios.13. A method of determining pulse rate comprising: receiving first andsecond intensity signals from a light-sensitive detector which detectslight of at least first and second wavelengths attenuated by body tissuecarrying pulsing blood; determining at least two values corresponding topulse rate based upon at least two different methods of processing thephysiological signals; and determining a resulting value for pulse ratefrom the at least two values corresponding to pulse rate.
 14. The methodof claim 13, wherein one of the different methods of processingcomprises a self optimizing algorithm.
 15. The method of claim 14,wherein the self optimizing algorithm comprises a least squaresalgorithm.
 16. The method of claim 13, wherein one of the differentmethods of processing comprises frequency domain processing and anotherof the different methods of processing comprises time domain processing.